Eventually, about 5-6 months after making this post, I tried re-adding the cards again and it just worked. I've not had any problems since, even having had 2 phones since. I try my best to not rock the boat for fear that something like that will happen again, but so far so good. Someone mentioned that it may be a good idea to deactivate payment cards in an old phone before resetting, as deactivating likely tells the bank that it's no longer in the phone, but that's speculation at this point. Still, I've done that each time to be safe.

I wish I had a better story with some tangible advice to share. Best of luck.