LOT OF FEEDBACK INCOMING
I disagree with most of the problems your listing. none seem to apply to shaco.
Stifling in lane (overpowered early game)
How? in AD form he does burst damage but is squishy and doesn't trade well in prolonged fights
In AP form you die if you follow him onto his boxes.
Uncatchable split pusher
So is zed, split pushing can be countered by simply being in the pushing lane under tower. it's not a good strategy as your relying on your enemys to react stupidly. if they react correctly you occomplish nothing.
Can lay traps that murder you without a chance to counter
Oracles lens turns boxes off
Assassin who can’t team fight
Only half true, yes he's squishy like any assassin is but the issue is you can counter his back line dive with pink ward and hard cc. His problem is invisibility being easily countered with a 100 gold item. its either really strong if he's invis or a massive vulnerability is he's seen, this is something wrong with the invisibility mechanic more so then shaco himself, riot need to add a damage reduction buff to champs while there invisible so even if there caught there not punished to the point of being one shot.
Permanent slow
Used to stick to a target, given his backstab damage this is needed, not a problem.
Ambusher who can’t be countered
Pinks, sweepers, warding deeper
Poor mid game
Agreed but why is his mid game poor? this is how to target an issue and solve it. is it his boxes having no scaling HP? does his mid game damage fall off if hes not snowballing?
Can’t carry well if fed
Again your pointing out an issue but not finding what's causing it.
Uncatchable if played correctly
This is actually a problem. The devs justify his squishy HP by how elusive he is. but pinks and oracles 100% counter this removing his strength and leaving him with only his balanced weakness.
Your Sub Goals
Lower early snowball potential
Now you're deciding what you want to do as a goal which is good but I don't see anything that describes what makes shaco snowball that your going to target
Increase dueling and assassination potential without making Shaco overpowered
Dueling and assassination are two totally different things, you can't increase them both at the same time.
Dueling is a back and forth damage trades with auto's and abilities, champs like fiora, Jax, Master Yi, Tryndamere are all great at dueling, they do consistent damage with no massive burst and use abilities to disrupt opponents damage output to give them an advantage.
Shaco isn't designed for this in any way. Q puts you in position for burst backstab damage. His W drops a box to deter enemy's from chasing him or to shut down an escape route, His E is more burst and the passive slows targets during gank's (the enemy is running full pelt at this stage and is NOT trying to trade damage but escape from the gank) and his ult allows you to gank up on an enemy or escape unwanted situations. I'm not going to discuss building him as a bruiser because that's simply not where he excels. you can stick armor on talon and make him a bruiser but it's not as strong as a full assassin build now is it.
Increase counterplay
You want to increase his counterplay? he's already rendered almost completely useless by pink wards and knowledgeable players who know how to spot the clone, that's everyone in plat and above btw. this is the exact issue with shaco atm. Players in low elo get crushed by him because they don't know how to counter him and he's pretty useless in high elo because players do. you give him buffs and he's balanced for high elo but snowballs like mad in low elo. he needs to stay at the same level of counter play but have LESS negative results when he is counter played (ie a pink spot's him and he's one shot, players ignore the clone and kill the real shaco)
GETTING INTO THE CHANGES
YES fix the shaco bugs
MANIC ATTACK
30% + 5% per level + 30% AP + Deceive passive + backstab bonus & slowing the target 2.5% per level for 2 seconds & gain movement speed 2.5% per level for 2 seconds
GOD THIS IS A LOT TO GO THROUGH.
For context I have to compare it to the old crit
Old Shaco 40% - 60% - 80% - 100% - 120% commonly scaled between level 8 - 13
New Shaco 30% - 35% - 40% - 45% - 50% - 55% - 60% - 65% - 70% - 75% - 80% - 85% - 90% - 95% - 100% - 105% - 110% - 115% between level 1 - 18
Stacked on top of that is + 30% AP (which I can't understand because full AP shaco's don't like to dive in for auto attacks and play him as a trap mage throwing daggers using his Q for escapes)
Stacked on top of THAT is the decisive passive (5% more damage per level) now i can throw this into the mix at the approperate levels we have
New Shaco 30% - 40% - 45% - 50% - 55% - 60% - 65% - 75% - 80% - 90% - 95% - 105% - 115% - 120% - 125% - 130% - 135% - 140% between level 1 - 18
My thoughts.
This is a horrible idea. So you carved out the damage from his Q, changed it to a flat damage buff instead of crit, made it more commonly occur with a reset mechanic. the result a ridiculous snowballing machine. Shaco's 20% backstab damage is part of the reason he snowballs and also starves. If he's fed its a 20% bonus to the great damage he's doing with his bought items, if he gets no kills its a 20% bonus to squat, he does little to no damage without items so the bonus is also bad. you've amplified that kit issue 10 fold. not only that its flat % bonus damage. so what happens if he crits??
check this out. let's say he's level 10 with a ravenous hydra and an infinity edge and crits with a backstab
Old Shaco
85 from his level + 155 from items * 250% from crit + 20% from backstab = 600 + 120 = 720 damage
New Shaco
85 AD from his level + 155 from items * 250% from a crit + 90% from his passive + 20% from backstab = 600 + 540 + 120 = 1260 damage
You honestly think that jump in damage is balanced??
What about if he's fed and has a trinity force too.
New Shaco
85 AD from his level + 155 from items + Trinity * 250% from a crit + 90% from his passive+ 20% from backstab = 600 + 480 + 540 + 120 = 1740 damage for a single auto. yep thats balanced :p
Q: Deceive
Cost: 90 / 80 / 70 / 60 / 50 mana 65 / 60 / 55 / 50 / 45 mana
You said he was too strong early and you just buffed him early. now he can Q for days.
Passive: If Hallucinate is active, Shaco can hold R then press Q to vanish in a puff of blue smoke, becoming untargetable and replacing himself with his clone after .5 seconds, and exploding it in the process. This reveals Shaco if he is stealthed.3
I have no idea what this changes other then let you explode the clone early which leaves it with No Counterplay something you yourself said shaco was lacking.
New Effect: Casting Jack in the Box or Hallucinate does not break stealth.
Your ult already doesn't remove you from stealth and casting a box while stealthed gives away your location. this does nothing and is not needed.
W: JiTB
Cost: 50 / 55 / 60 / 65 / 70 mana 40 / 45 / 50 / 55 / 60 mana
Again buffing him early letting him slowball.
Cooldown:~~ 16 seconds~~ 10 / 12 / 14 / 16 / 18 for each consecutive box
You just removed top lane AP shaco from the game
45 / 60 / 75 / 90 / 105 (+ 15% AP) (+ 5% bonus AD)
The issue with boxes isn't their lack of damage but the consistency of their damage. this is not needed and further removes AP shaco from the game. now you don't need AP just AD and levels.
Passive: The cooldown for Jack In The Box is increased by 2 seconds for every Box that is currently active.
Passive: Up to 3 / 4 / 5 boxes (At levels 1 / 6 / 11) can be placed at one time. Expired boxes, and boxes exceeding the limit, disappear in a puff of blue smoke (not seen through fog of war).4
AD jungle start is ruined but clear speed becomes faster after level 1. shaco can no longer early invade or gank faster than any other jungler. there are now less reasons to play him. an unneeded and probably unwanted change any shaco main would hate to see.
New Effect: Boxes prioritize Shaco’s current target.
Boxes already do this.
New Effect: Boxes now take 75% reduced AoE and DoT damage during the 1.25 second delay before they enter stealth.
They can still be one shot by champions and monsters, this doest fix shaco's team fighting at all, boxes would need scaling HP to work in team fights.
New Effect: Boxes are now placed instantly (easier to block predicted skillshots).
Nice interesting idea adding more skill and depth to the champion.
New Effect: Clicking on Shaco shows how many boxes are currently placed.
Gives away if he's real or a clone?
New Effect: If Jack in the Box is not placed in brush, it will quietly cackle with excitement once an enemy is within its laugh radius. This effect can only happen once per box.
Why? what possible buff or nerf does this offer? it gives away that shaco is nearby ruining his invasions and laning tactics.
My Thoughts
Your removing AP shaco from the game and ruining his jungle start, I have no idea why? ruins his laning as well seen as the boxes gives away there presence with a laugh. this change is unneeded, unwanted and I don't see a point it in.
boxes are not teemo shrooms, there damage stacks so making them last 120 seconds is absurdly OP, there free wards too. massive buff with no counterplay again.
E: % Max health damage
Nothing more to be said, your not reworking shaco your buffing everything he has.
R: again % missing health damage and further movement.
This is NOT a rework. you just buffed everything shaco has and called it a rework
I would suggest you scrap everything and start again. find the root of shaco's issues (his dependency on gold which as a jungler he can't get, his passives fluctuating value depending on if he's snowballing or not and his lack of late game scaling due to box's damage being unreliable and his lack of escapes from teamfights)