I'm not sure what exactly reworking the jungle further is going to do to influence people to play "carry" junglers over "AoE" junglers. The whole point of your ideology is "We'll make one monster harder to kill, and the rest way easier and it'll speed up single target junglers!" it really won't. It just means that they spend more time on the bigger monster, taking more damage and less time on the smaller monsters. AoE junglers will always be significantly faster than single target, that's the way it is. They have a persistent primary, and secondary damage source.

Example: Shyvana - Persistent damage: Burn out
Secondary damage: Auto attack.
Potential secondary damage bladed armor

Her DPS at least the way I run her is 41ps from burnout and 77 .7 times per second which is 53.9 DPS essentially. Then bladed armor which is 6 true damage per auto attack from monsters, which with wraith attack speed at something like .7 is 4.26 DPS. So Shyvana's total DPS in the jungle on the biggest monster in the camp is roughly 99 DPS at level 1.

Say the big wraith at the camp at level 1 has 600 hp and the small wraiths have 180. (More example I main jungle never took the time to track their hp)

Assuming she gets 0 help from anyone, For the first 7 seconds of this jungle clear burnout is active, her secondary DPS over 7 seconds is 41+4.26 so, 45.26 DPS to the small wraiths, it would take her about 4 seconds to kill all 3 of them. As for the big wraith having 600 hp she deals 99 DPS for 7 seconds This is 693 DPS in 7 seconds to the large wraith. It essentially takes her 6 seconds to kill it (I'm aware the real time is about 9 1/2 seconds or so it's more example math)

Now let's take someone like let's say.... Fiora. Assuming you're running a full on AD page and you start with W first you sit at like what 92 AD? And about a .71 Attack speed you're getting about 65.32 single target DPS. Now chances are, if you're running a 21/9/0 carry master setup for your defense you're most likely running sum. resolve, durability, a couple pts in hardiness, and vet scars. So you dont have bladed armor. Your riposte damage is 70 or so on like a 12s cooldown. It amounts to 5.833 DPS. So Fiora's single target DPS at level 1 is 71.15. She has to kill 4 creatures for a total of 1140 hp. It's going to take her 17 seconds to do so.

This is just a statistical reason why no matter what it is you do, AoE junglers are always going to outsurpass single target carry junglers. With the only exception being, if you keep raising the big monsters health Dr. Mundo and Shyvana are just outright not going to be able to clear anymore, I mean hell, Shyvana already clears wraith/red/golems/wraith/wolf/blue with 0 health pots, and about 340 hp left. Not to mention she gets incredibly low in between(Mind you I run either 9/21 or 14/16 depending on my mood on her). So your only saving grace is DPS stacking them out of existence.

Other than that, even if these people couldn't jungle anymore, carry junglers are still not going to exist. Here is why.

Top lane is reserved for a select group of folk.
-Assassins
-Bruisers
-Bruiser tanks (Shen for example)
-Split Pushers

Their one thing that they generally all follow in common with is that they can dive onto an enemy ADC. Sure there are a few who cannot but they're incredibly effective at split pushing, and clearing minion waves (Like singed) and there is no major draw back from them being over extended. They are incredibly tanky and mobile so getting ganked even when way far out is not a huge deal to them.

Mid lane is reserved for AP mids their role is to dominate the early game and mid game. They're generally pretty squishy, and don't make good junglers with the exception of a couple.

Why is this relevant? Because it leaves 2 places for tank initiators. The support role, or the jungle role. As a rule of thumb supports tend to make the absolute least gold in the game, by a pretty fair margin.

So then the question is posed, how would you rather take your initiator? tanky and farmed up because he's been in the jungle for some time, he's been picking up kills and assists all over the map, and he's able to generate a good amount of gold, or would you rather your support initiate, being deprived of farm in the name of assisting the ADC with gold gen, being squishier with more team oriented items, rather than particularly tanky items?

This is where the AoE junglers come in. They are all good initiates, many of them have great tools to isolate champions, put down crowd control, and just be a menace, with little to no regard for their own personal being, because if they've done their job right, they can handle a 5 man focus long enough for your team to just eviscerate the enemy team. So who cares if they die? Here is some good examples of what some tanky junglers can bring to the table

Shyvana: Dives balls deep into the heart of the enemy team, with high mobility a cone armor debuff, a large damage output between burnout, twin fang, and just being built strong like a truck.
Shen: Deals good damage, can take massive amounts. Has a line AoE taunt which excels in close corridors, and can initiate on top of a top lane bruiser who's leaping in like Lee Sin/Jax from anywhere on the map. Not to mention he split pushes with no regard to well being because he'a a great duelist.
Nautilus: Is just one giant ball of CC. Has a passive root every like 8 seconds per target, has a massive AoE slow, that can strike multiple times. Has a short cast but long range line knock up that can hit multiple targets, and has a pull back.
Amumu: Has a skill shot root+stun. Some fair damage output, and an AoE team lock up and can reduce enemy MR significantly.
Maokai: Has a root, A line Knock back+Slow an AoE damage reduction, that can be recast to deal damage, and short timer vision revealing spell that deals damage and great sustain with his passive.
Mind you 4/5 of those are what I'd call AoE junglers. Also consider Cho (Vorpal spikes) Nocturne (Umbra Blades, if you run attack speed on him the cool down is like 5 sec.), Skarner (His Q smash's high damage, low cooldown) Dr. Mundo (Burning Agony I believe it's called)

Now lets see what the carry junglers you're pushing so hard for have.
Master Yi: Can run really fast once he hits 6. Has a gap closing Q, and a crappy heal (unless played AP) would get decimated diving into a whole team first. NEEDS red buff to gank. Gets shut down pretty bad by hard CC. Has none of his own
Tryndamere: Has a heal, and does a lot of damage and has crits. Has a potential slow thats not terrible, and an AD debuff. Has a line AoE damage gap closer that's really nothing special. Would get decimated diving into a team for initiation but would probably force some CC to burn through the 5 second hassle of his ult. Gets shut down by CC and has an incredibly unreliable CC.
Gangplank: One of my personal favorite champs, and probably the most viable. Has a giant AoE slow that can be cast anywhere for initiation. Has a passive stacking slow+DoT. Is the most run-mobile champion in the game getting like 430+ movement speed without any movement speed items once you max E. Can initiate his slow from a safe distance. Has a great heal+debuff remover. Can viably build tanky and deal damage.
Fiora: Has crappy chase, even with her E stacked. Does deal a lot of damage, and can tower dive pretty safe @6. But her ult is incredibly long cool down, and her ult can put her in incredibly dangerous situations and she gets shut down by CC hard. Could initiate I suppose with ult, but unless she's fed she's not going to do anything major and she's going to die once she comes out of it.

Want "Carry" junglers to be more relevant? Put some food on their table, let them bring something to the team other than the unreliable potential of stupid amounts of damage. Like seriously tank junglers tables look like it's Thanksgiving 24/7, while carry junglers are village fisherman in crappy waters. Every once in a while they may come back with a big catch, but most the time the family is fighting over one fish.

Would like to note mid is also for some AD assassins who's goal is generally to bully AP mids around and prevent them from dominating the early and mid. And also to help roam and snowball other lanes.

In reality no carry jungler is going to be viable without being over powered. If you put high AoE damage, CC, gap closers, and pretty much everything they would need all while having insane damage they would be over powered as hell.

In fact I remember a carry jungler getting released a while ago that had AoE CC, good tankiness, extremely high damage and a refreshable gap closer. She was the most over powered champ at release in recent memory barring perhaps Jayce. Surely you haven't forgotten release Diana?

Honestly I think they need to accept some roles are what they are. The jungle really isn't meant for carries and trying to make it work is like trying to fit that square peg into a round hole. Either it's to small and goes right through with no effect, this would be tryn/yi/etc, or to big and breaks the hole, see Diana.

Honestly Diana wasn't as over powered as people like to think lol. She had a 51% win rate. There are a few "Balanced" champions with a 52-53, infact Taric has like a 54 or 56% win rate. Highest in the game, and he isn't an "OP" support. When they nerf'd Diana she plummeted to an average 40% win rate lol.

Anything short of making a like 300g monster effected only tiamat that does like 40%-20% AoE for auto attacks and can only be used on single targeters. is never going to make them more viable than tanks just in the matter of jungling.

Plus you look at Shen who isn't an AoE jungler who still gets picked over the "Carry" junglers because he brings more to the table jungling.

I think the most important part of this post is the following quote:

"The whole point of your ideology is "We'll make one monster harder to kill, and the rest way easier and it'll speed up single target junglers!" it really won't. It just means that they spend more time on the bigger monster, taking more damage and less time on the smaller monsters."

Deirin you know you can quote specific areas not the whole post right? But no adding more hp to the big monster really doesn't change the speed of an AoE jungler.

In fact in S3 with much stronger monsters in the jungle Shyvana clears about 3 seconds faster overall, and so does Dr. Mundo because the camps have the same amount of total health as per my wraith example where the total health in the camp is 1140 no matter what way you spin it. By increasing the HP on the main monster, thats THEE only monster you have to focus on. All the small wraiths simply die to collateral damage still. You're still dealing that persistent amount of damage to the monster while auto attacking it. You're only going to change an AoE junglers clear time by about 1 second without being overboard, and it's still going to make a single target jungler the same speed, and take a significant amount of damage more than he normally would.

The biggest problem is, there's only about 4 junglers presently who can clear with health potions left on Machete/5 start. Shen, Skarner, Cho'Gath, and Trundle. Most the others clear with none and incredibly low hp.

So where exactly do you put Udyr, who is one of the best AoE Junglers but lacks the dive ability and has very micro intensive CC?