I've been going on aamc.org pretty frequently checking out dates and what not. September 22nd is the deadline for the lowest fee for changing a test date. I would keep checking. I got lucky and got a date set for Oct. 25th, which I am not ready for, but nonetheless I don't have to wait for April! Good luck 🙂
P.S. LA state shouldn't be too bad getting spots, it'll open up..just keep checking!