If you can beat the first endgame rematch with five puppets, do it with a reincarnated black mark Kogasa in your sixth slot. Keep doing this until she gets to level 70. Once she's there, style change her to Assist and set her ability to Warning Shot. Assist Kogasa has a fairly easy time setting up on Speed Mokou and proceeding to solo the first fight; once you have her able to do that consistently, build up a Power Aya. Equipped with the Art of Combat, dual multi-hit STABs, and Earth+Electric coverage, she can solo the first three fights with zero set-up once her level is in the high 90s, and will only take a single hit per run.
Being able to solo the fights is very handy for grinding, as you can load your party with five mons that need training and build them all up at once. It's also faster to run down the halls to the next fight than to gap out and re-enter, which is why Power Aya is preferred; she needs to be very high level to do it at all though.