The atma's impaler upgrade is way too strong... especially with warmogs being as strong as it is right now. It would destroy the game and make bruisers unstoppable. And the quick silver sash upgrade sort of replaces abyssal sceptre too much (also, 60 ap? I think you mean built from a blasting wand bro)
To properly implement it, you'd probably have to change abyssal to give less mr and more ap, and give yours a bit more mr... and possible drop the tenacity or spellvamp (just imo there, as with mecurial you get 100% move speed for 1 second if you are melee, and no change otherwise)
I do like the other idea although possibly changing it to include, maybe about 10% cdr for a bit of extra gold might help because the stats feel too low for the price considering the passives are just glorified mana regeneration.

Ancient Sash [Legendary tier]
-Unique Active: Removes all debuffs from your champion,
your champion gains 10% Spell Vamp and for 5 seconds (90 second cooldown)
scimitar doesnt have crowd control reduction
else mercury scimitar should also have cc reduction
scimitar also doesnt have lifesteal but i think 10% spell vamp isnt big deal

Cursed Impaler [Mythical Tier]
+ 500 HP + 45 ARM + 20% CRIT CHANCE
better more health than armor since it benefits from health as damage

my example for The Warrior's Mug would be
+15 mana regen / 5s or +10 mana regen / 5
+40 mgc resist
- Unique Passive - Mana Font: Increases your mana regeneration by 1% per 1% mana you are missing.
unique: +1 attack damage for every 2% missing mana
chalice gives enough mana regen so getting mana vamp would be too much
and with less damage you would become less effective
and mgc resist would be up to 40 because you dont want to get melted by mages
(the mroe the better ^^)

obviously you didn't read what I quoted.. and then adjusted.. the item fixes are in the quote itself.. check them out.

About scimitar not giving cc reduction that's true.. however it does give a movement speed boost for 1 second. Given that your ranged id assume having it give tenacity for 2 seconds on the active would be better. U could also just give it 1 second of movement speed.

To note on the ad chalice.. it doesn't steal and give you mana.. it steals and then heals you for the amount of mana stolen. So it would help ads drain off the ability of spell casters to cast spells.. but in a limited way but also give you some form of active life steal.. kinda like how the current BotRK gives you an active damage to heal effect. Also it could be unique in the fact that no item drains another characters mana ATM.

I wont argue about black cleaver being more powerful if its the only item that you build. However black cleaver has health and there forth stacks with atma's even if minutely. Plus giving health to atma's is redundant since its passive scales from health.

However almost always if im building a tanky or off tanky character (assume your support or jungler is tanky, then I find the passive armor and Crit with the added ad to be incredibly useful. To note, I personally build atma's anytime im willing to build warmogs.. they synergize way to well with each other.. also they nerfed atma's it used to give 2% of max health.

(note Tankplank/Critplank build is expensive but is offset by GP's passive. If you can farm top lane and Q farm thats 8 extra gold.. a minion + 2 extra gold from Averice blade.. 10g a minion.. you farm 30 minions you just farmed an extra 300g thats 5 waves of CS. Also generally speaking as GP your ulting your allies team fights not your own giving you massive gold gen via assist.. I not uncomonly go 5, 5, 25 on GP at the end of a game.

Also.. on the Impaler.. 500 health is exactly 7.5 damage.. youd get more benefit from the passive 10 Ad off scepter also you would get 10% lifesteal which could be huge if your already tanky.