I don't know much about this Kakuzu character, sorry(couldn't find much helpful footage either).
Not sure what you mean by becoming the puppet when talking about his ult.
My idea is an ultimate that buffs a puppet on a short cooldown.
I also rethought each puppet to have a more controllable active skill rather than depending on an AA rotation for half of their effectiveness. If you prefer your own versions maybe we can think of similar buffs that the ult could give them. As for what I did to them, I wanted to keep the high skill cap you talked about while trying to make it feel more like you're controlling their every move yourself like puppets rather than just ordering them around Azir style.
Here's what I ended up with:
Passive:
While a puppet is active, the ability that summons it can be reactivated to channel for 1 sec before making the puppet perform a special skill.
This costs half the mana and has double the cooldown of the ability that summons the puppet.
Each puppet will also generate stacks when performing certain actions, giving them bonus effects.
Q: Summons a melee puppet with a lance and shield who can proc your own on-hit effects.
Cooldown:5s Cost:/60/80/100/125/150 Mana
Gains 1 stack when it is auto attacked by a champion or large minion.
When it has 3 or more stacks, the next auto attack that hits it will be blocked by the shield, consuming 3 stacks.
Special Skill:
It dash up to 400/500/600/700/800 units in a chosen direction.
The 1st enemy or neutral unit hit stops the dash and is impaled by the spear dealing 70/90/110/125/150(+ 50% of the puppet's AD) Physical Damage and is snared for 1sec. If there is another target behind them within melee range, the spear extends to stab them dealing the same damage.
Puppet Stats(they scale with your stats):
HP- 500/600/800/1100/1500 (+ 60%AD, +40%AP)
Attack Damage- 65(+100% BONUS AD, +50%AP)
Range- 125
Ability Power- 0
Attack Speed: 0.654(+0.2692 per rank)
Armour- 20/30/35/40/50 (+10%AD, +5%AP)
Magic Resist 30(+10%AP)
Movement Speed 310(+10% AD, +10%AP)
W: Summons a wizard puppet whose Auto Attacks instantly damage the target and deal an extra 40/40/60/100/150(+20%AP, 60%AD) magic damage.
Cooldown: 4s cost: 80/100/120/150/180 mana
Gains 1 stack when it auto attacks.
When it's special skill is used, its cooldown will be reduced by 1 sec per stack. That many stacks are consumed when this happens. Any excess stacks will be consumed to restore 5% of your missing mana to you for each.
Special Skill:
Creates an explosion about the size of Soraka's silence thing.
The explosion deals 80/85/95/110/130 (80% AP, 10%AD)
The cast range of 550 units is centered around this puppet.
Puppet Stats:
HP- 500/550/660/800/1000(+ 105% AP)
Attack Damage- 40(+ 55%AD)
Range- 450
Ability Power- 0(+100% AP)
Attack Speed: 0.654(+0.2692 per rank)
Armor- 0
Magic Resist 30(+10%AP)
Movement Speed 310(+10% AD, +20%AP)
E: Summons a ranged jester puppet who's Auto Attacks slow the target by 10% for 1sec and deal an additional 30/70/100/120/130(+ 5%HP, + 30%AP), but this cannot hit the same target twice within the same 10/9/8/7/6.
Cooldown:0.5s Cost: 50/75/125/200/275
It gains 1 stack every 5/4/3/2/1 second it remains within close rage of an allied champion(let's say 300 units).
The special skill is only available for as long as you have at least one stack.
Special Skill:
You channel while it gains a 10% movement speed buff and plays music.
While the quirky tune is playing allies within a 400/450/500/550/600 unit radius of the puppet regenerate 2/2.5/3.5/5/7(+ 2.5%HP, +10%AP) percent of their their missing HP per second. This can affect your other puppets.
The Jester puppet cannot attack during this time.
Puppet Stats:
HP- 500/600/800/900/1100(+ 5%HP, + 10%AP)
Attack Damage- 53(+5% HP, + 5%AP)
Range- 500
Ability Power- 0(+ 90%AP)
Attack Speed: 0.654(+0.2692 per rank)
Armor- 10/20/30/35/40(+ 5%HP, 7% AP)
Magic Resist- 15(+8%AP)
Movement Speed- 330(+6% HP, 4%AP)
R:
Passive:
The soldier needs one less stack to block an attack.
The wizard's attack range is extended by 100.
The Jester gains 2 stacks upon slowing a target with it's auto attack.
Active: Usable only when a puppet is active. That puppet's special skill is altered until the next time it is deactivated.
Cooldown:60/55/30 Cost: 120/110/100
Alterations:
Soldier: Stuns rather than rooting 1st target hit. Damage is also increase.
Wizard: The Explosion increase in size greatly(to about 500 units radius).
Jester: Besides the healing, each tic of the AoE applies to enemies the slow from his auto attack passive, and half the damage.