No offense, but it feels like a good deal of the PBE is extremely incompetent. I'm not even saying I'm a good player, but anyone I've played with/against have just been head over heels retarded.
That being said, there isn't any real way to actually test this on the PBE server.
Either way, double jungle sounds terrible. As it is now, jungling is still extremely slow. The banking system helps it out a little bit, but if you're constantly killing them with two junglers, they're not going to be banking very much.
Invading the enemy team is usually pretty stupid as it is now as a single jungler. If you're playing against players who actually understand how to ward, you'll never be able to cross the river without the other team knowing. Even if you bring flash and exhaust, they will each only help you once every 3 or 4 minutes, which doesn't give you many options while they're down.
In terms of laning, the bottom lane 2 could very easily deny the 1. The number of people in a lane does not constitute faster pushing if you're playing against people who actually understand the concept of last-hitting. As long as they don't push the lane up, they can easily deny the 1. Either that, or they could just very easily push the tower down extremely fast, while the gap between exp is still too little for the 1 to be able to stop them, and both junglers are busy gimping themselves while they wait for the small camps to respawn on their side of the jungle. Not many junglers can actually gank at level 2. (Nocturne, Rammus, and Fiddles, all pretty half-assed. Pretty much only Lee Sin.).
Lastly, your proposal does not actually leave much room for a decent team comp. If only tanky characters are allowed into the top and bot lanes, that leaves AP, ranged AD, and support to be jungling and mid. No matter how you arrange that, one of your most important damage dealers are taking smite over something that would suit them better, or your support is bringing heal/cv/smite without any room for escape.
Right now, the PBE isn't that far from Live in balance. If you actually want to see this happen, find a friend to duo queue with. Better yet, find a 5's team, get high elo, and make it the "new meta". See how far you can get in ranked, and prove me wrong.