Well then I don't know what to tell you.
Everything pretty much points to dropsy. The whole fish doesn't have to look like a pine cone in the beginning stages of dropsy. Dropsy is mainly caused by poor water conditions. I understand that everything came out neutral with no ammonia, etc. But the fact that he turned red and had inflamed gills up until his death points to it as well. Turning color also shows a sign that he's sick, and depending how red he turned, can
be ammonia burns. Dropsy (the symptom) is not very contagious to other fish, if at all. The bacteria that causes dropsy, however, is contagious. There could be a bacteria in your tap water or maybe something got into the water, like lotion from your hands or cleaning sprays or air freshening sprays.
Also, poor water conditions also highlight your fin rot. Fin rot can be bacterial or fungal. The fact that the fins were turning black shows it was bacterial. There is bacteria in your tank that your other fish, since they are healthy, have the immune system to resist them (so far).
I understand the first link is for goldfish, but dropsy is dropsy. It does the same thing to both bettas and goldfish.
Last link talks about goldfish again suffering from dropsy. It mentions something about its gills bleeding (which do flare). Typically, a fish's gills stretch when in distress.