Brook was clearly affecting the other Homies since BM needed to send Zeus and Prometheus and her hat at him though. That alone would eliminate a big chunk of them from Luffy's attention thus saving his stamina.Brook with that advantage only managed to land a boo-boo on Promotheus and none of the other Homies even had marks on them.
I don't recall the fight well enough to go into detail without refreshing myself on it and I don't have that time right now.
I agree the vivre card probably wouldn't effect the big 3 since they come directly from BM(I wonder if she'll be able to "revive" 3 times in a sense where she can take the soul back from Prom., Zeus and the hat?) I didn't remember Nami losing that, I wonder if it'll come back at all or if it's part is done, probably done I would guess.Amande also took the Vivre Card from Nami, which in all likelihood wouldn't affect Big Mom's Big 3 Homies anyways. Brook could straight up exorcise the Homies while the Vivre Card just prevented them from attacking, it's doubtful that card could affect the special Homies anyways.
Unless she has some serious strength tucked away we can safely say Luffy passes her in power, so if her biggest(strongest) known attack has little to no effect then the only thing I could see helping her win is a power unknown to us as of yet. This may end up just another case of good DF match ups for Luffy, if BM's DF becomes ineffective against him we could have another Enel situation where his opponents main strength comes from their DF.We have no idea what the full scope of Big Mom's powers are. That technique might not work on Luffy, but do we know that none of her powers will?