Man, I had an old hand tell me the same thing years back. Something like "the weld starts before you pull the trigger." Blew my mind how much time I was wasting fixing stuff I could've caught in 5 seconds.

Patting them dry is a must, skipping it steams the skin instead of crisping it up.

Did you salt the soaking water or the cooking water? That's the thing that gets people every time, because salt in the soak actually helps the skins stay firm while the inside softens up, but if you add it too early in the cook with an acid like tomatoes you're asking for trouble. Chili is the worst case for this since you've got all that tomato in there breaking the beans down on day two. Try cooking the beans plain in salted water first, then add them to the chili when it's almost done, and keep them in their own liquid in the fridge instead of swimming in the sauce overnight. Also how long are you actually simmering them, because 6 cans worth is a big pot and the ones at the bottom are going to keep cooking from the leftover heat. Smaller batches fix it too but then you're back to cooking every few days, so I'd rather just nail the timing.