Sorry for the very late reply, but so very happy to hear I'm not going crazy!
It sounds like you've figured out your own horribly annoying fix. I'm basically doing the same thing, but I'm manual saving because I'm afraid of the game auto-saving after simming a ton of games: I manual save (creating a new file) after every series, and if "Play My Next Appearance" starts simming a bunch of games in a row, I just quit the program and start it up again and load the manual save. (Simply backing out and re-loading my save doesn't seem to work. I have to restart the game.) After that I'm good for at least another series, sometimes two or three.
Annoying as hell, but at least the game's still playable. I've put a lot of time into this career and I'm really enjoying RTTS for the first time in years, so I want to keep playing!