Well I beat em. but yeah, none of the mentioned strategies were worth @#%@#.
First off, I don't know why, but my sakuya can't hit eirin, skills or not. The only one that ever hit for me were those 2mp "nukes" that can debuff...They never would though. Controlling Kaggy also rarely worked. I had byakuren equipped with the best scroll available, had much induction, even worse a +30 induction accessory, and casted hyper trigger on herself, but control/charm would fail 8 times out of 10, and the few times they did work, they would normally only last one turn, making it useless since kaggy tends to cast something bad after being controlled on that turn anyway (sometimes, it's odd, it's like the game isn't sure if whatever she casts is supposed to be on my side or hers), and no, I wans't meleeing her while controlled.
Nitori with the slayers and radiate was the FIRST thing I tried, but yeah, she'd miss alot (less than sakuya thankfully), and despite the slayer effect, her hits wouldn't do more than 300 total. I had more luck using sunny flare or whatever it's called, would hit 200ish, both people and wouldn't miss. Marisa with slaying lasers was what i mentioned earlier, would hit for about 500 to each. 900 if I buffed her and kaggy did NOT buff herself, but 200-400ish if she did. It was all very doable minus the whole kaggy can heal herself completely part. In the end I found that I had better luck forgoing using marisa's lasers, and using patchy+ marisa instead for patchy's elemental land buff, Patchy could do fair damage, and Marisa did the same as before (500 base 900 buffed, 200-400 kaggy buffed), only her elemental nukes cost only 3mp if I need economy. I also needed luck on my side to make sure kaggy didn't offensive buff + eirin starlight arrow, There still seems to be no defense against that. At one point kaggy did offensive buff, and eirin used "apollo 13", which I thought would be an even BIGGER oh shit situation, but thankfully it wasn't >=).
One thing I've noticed about this game which is odd, is that as I go further in the game, it seems like enemies drop less Power. I figured it must scale by level or something, but no. I went back to the SDM, and I'd end battles with over 10 power rewarded regularly. But there are many tough fights in current content that still drop something stupid like 3-4! This means that if you level grind earlier in the game, you'll actually be more powerful if you do it later (unless it grows back up again later later), even if the end result levels are the same. Unless you level grind old content that is.