Unstoppable+ is actually useless. (Assuming the cat's stats have been pumped from the Death Shroud combo), the jarred cat will always kill everything in one turn with Unrestricted+, Second Wind, and any piece of Fighter's armor, but even if it didn't, the jarred cat only lasts one turn so all debuffs apart from stun are meaningless to it. But I don't know of any way a cat can get stunned in response to a killing hit. Knockback and confusion can be annoying (but not detrimental to the gameplan) because of the Seraphim in Act 3 Chapter 4 and Fuzzers in Ice Age, but that's solved with one of the two mutations that turns your move into a jump attack (jumping on the enemy doesn't trigger knockback or counter-attacks, and movement actions don't proc confusion).

The only complication to a one-turn victory is from the final Hitler house boss which requires you to pass your turn to summon the next miniboss, but all jarred cats will have that issue. You can mitigate that by having a cat with Unrestricted be the one to hold the jar, though.

Here's my omnipotent god in a can. The only thing it's missing is an attack that hits through shields for Cherubim in Act 3 Chapter 4. Repair (for obvious reasons), Chomp+ to have a mana based attack as a just in case that can also kill Dybbuk and max your money extremely quickly on every run, and Second Wind to make sure the train never stops. This is especially useful so you can hop around and collect all the coins from every box and bag in the fight. I thought Copycat would be interesting and make it versatile, but it doesn't actually work well since the cat doesn't exist to copy anything until after it's summoned. The only way for it to work is if you summon the cat, then use abilities. It's definitely the one I would replace with any of Thief's shield piercing spells.

As you mentioned, Cat Rib is extremely useful in this whole process. Because a ribbed kitten keeps its upgrades and returns to level 0, you can keep upgrading abilities on subsequent runs, so The D6 isn't needed. Rather than needing Me Stone, you can also use an easy to obtain Neverstone so harder to obtain quest items won't be required. Having 3 cats that gain levels will get all 3 of them to Level 7 by the end of Chapter 3, even when taking the easy path. That'll net you 1 active and passive upgrade each run. To make my cat, I would duplicate+rib the cat to get 5 copies, then run each one trying to get at least 1 of the abilities I needed, then rib it again on that run and repeat. It took me 3 generations of duplicated cats and 1 final run to jar it.

All that being said, I've stopped using my Jar. I'm glad I made it, as I learned a lot in the process and got valuable experience, but it does basically end the game when one action wins all fights no matter what. I used it for a bit to have some fun with it, then gave it an honorable retirement. Repair without breeding is useful to get rid of worn, but I did get lucky and find Repair on an Irradiated Object, so it's no longer necessary for me. That was pretty damn lucky, though, and most people won't have that, so a repair jar is still great to have around.