This has been most helpful! Apparently, a new script I added to stop the timer whenever you're reading something or sitting through a cutscene has been messing with how the New Game+ works. I've fixed all of the issues you were having with the timer running out during battles, as well as the hopeless loop all New Game Pluses were getting caught in. I'm going to see if I can somehow rescue your New Game+ file.
The bug that happens when someone leaves your party is a bit stickier, though. I'm trying, but I can't seem to fix it. I think it's an issue with the Yanfly script not playing nice with some other vital scripts. I'll spend some more time on it, but it might not be fixable.