Countering Nihilus led Dooku squads?

Tbh I don't think your team can take him, especially 88's healing immunity is bugged, so for now just avoid these teams.
There are many counters out there, stun, daze, shock, healing immunity, annihilate and wiggs triple shot.
If you don't want to change your entire team, bring in a stunner like royal guard and don't AOE until he is stunned. Or farm 5 rebels to five stars and unlock ep, he will be a great counter.

I have General Grievous unlocked, would he be useful? Or is his heal immunity bugged as well? I figure the health down could help counter the high health pools of Nihilus teams, heal immunity (if his works on health steal), and his basic can't be countered.

I don't think his heal immunity is bugged, but you can't rely on him countering DN/Dooku because he is too slow relative to Dooku so not enough damage from his basic, also his heal immunity is on a special with 4 or 5 turns cool down and 65% chance is not reliable i.e if the debuffs didn't stick you'll have to wait 4 turns to try again.

Your JKA might be useful. His heal immunity could help, but honestly I face some DN Dooku teams and use that and it is a little unreliable. I have Yoda to back him up so if he can't "stick it" I can stun under 100% health. Aayla might be a better option with her stun, but its also not a "hard" stun. The only other option is Daka, and having a healer in your arena team is suicide if you want to climb...

The best team I found to counter a Nihilus lead Dooku team is a Nihilus lead Dooku team with a lot of health. If you can focus on Nihilus and kill him before he uses annihilate, and use your annihilate on Dooku you could win almost every time. I use Sidious and hope he can lay down healing immunity on Nihilus at the beginning. And I use K2 for the vast amount of heath and his taunt and counter. Fifth team member just needs health and high damage. Not sure if you have those guys in your inventory, but that seems to work for me.

I'm also a droid user F2P lvl 79 and I get to beat them when I don't get fucked with RNG like 86 ALWAYS picking JE to assist with his special or when HK-47 doesn't land any debuffs after his special (I'm always around top 100, can't get more than that because of the same reason). My attack order is 47-88-86 and I use boba, I managed to unlock R2-D2 which I'm already gearing up since stealth doesn't trigger counter attacks and the burning will help out a lot along with the stuns on his basic, I'm hoping with this I can solve my dooku problem and climb at least till top 50 like I used to be before nihilus appeared. In the meantime I'm gearing up my siths too cause when my shard starts to get the zetas and stuff droids will be useless anyway until a rework for GG or something. So yeah, if you didn't get R2-D2 gear up a new team, like rebels with wedge+biggs or a sith team or an empire team with the troopers which are awesome now (shoretrooper a pain in the ass to get for us still tho)