I've been so consumed with betta diseases, betta, illnesses, betta problems, that I forgot they are, after all, FISH. So I went back to everything I've learned from my koi over 12 years, and now believe that my bettas had gill flukes, which came in on the moss ball. Which I stupidly moved from tank to tank. All my fish had the same symptoms of sitting on the bottom, trouble breathing, and sudden jerking swimming.
Thanks to a search here, I found the procedure for a salt bath, which I will promptly do :) Hopefully salt will kick the gill flukes butts, and I can start over again. If not, I'll have to get out the big guns :(