Looks like tail biting to me, I apologize, but I have to admit that I did not read the whole wall of text you posted, so excuse me if I'm going over something you've already been told.
First of all, stop giving him antibiotics. You never want to give a fish antibiotics unless you are sure they are sick, or you will make
them sick. They are very harsh medications that are likely exacerbating your problems. Please read and understand the information in this article before ever using antibiotics again:http://edis.ifas.ufl.edu/fa084
it will help you understand the risks involved, how to use them appropriately, and why it is important to be responsible about their use.
Second, are you treating the RO water with a remineralizing product like Seachem Equilibrium? You must treat the water because it is so pure that it lacks vital minerals that contribute to the health of your fish and buffer pH.
Due to overbreeding, stress, and their confinement in small spaces, many bettas develop destructive neurotic behaviors. This is similar to dogs and cats that have been in a kennel too long without stimulation--many of them overgroom themselves and walk in circles compulsively. Bettas do the same thing, in the form of glass surfing, neurotically swimming back and forth across the same area over and over, and tail biting--self mutilation of the fins. If the fins are ragged, tattered, and uneven, it's likely that the fish has been biting himself. Many owners never see their fish do this because their presence is usually enough of a distraction to stop them from doing it.
Fin rot, on the other hand, usually originates from ammonia burns on the delicate, thin tissue on the edges of the fins. The burns caused by the ammonia develop a secondary infection--fin rot--which turns the edge of the fin black, gray, and crusty or fuzzy. The edges are usually smooth and the infection usually moves quite slowly. It will take days for fin rot to make any significant advance--it's not as if you could go to bed and wake up to a horrible rotted up fish. The infection simply does not move that fast. A fish biting himself can tear out large chunks at a time, and yes, they can reach to bite themselves all the way to the body if they wanted to.
Wounds inflicted by the fish biting himself can be infected with fin rot, too, although if you're keeping your water clean and doing proper maintenance, it shouldn't happen. Look for the dark coloration on the edge of the fin to determine if he is actually infected. Clear or whitish edges are a good thing--new fin tissue often comes in clear or whitish and colors up later.
In each case, consistently clean water is all you need to get him to recover. Warm temperatures and a high protein diet will help him build new fin tissue faster, although halfmoons tend to regenerate slowly due to the complicated structure of their fins compared to veil tails and plakats.
To stop him from tail biting in the future, you have to get to the root of what's causing him to bite. Finding his "trigger" can be quite difficult, each fish is an individual, so there's no blanket recommendation I can give you except to try to examine his living situation for possible signs of stress, such as temperature fluctuations, proximity to another betta or something that looks like another betta (like a brightly colored sheet of paper nearby or a poster), too much traffic in front of the tank, proximity to electronics, too much decor in the tank, not enough decor in the tank, too much filter current, etc.
I have had two tail biters in the past--it took me weeks to figure out their triggers. For one, it was that he hated to be in total darkness at night. Once I added a dim light to the room at night, he stopped biting himself. The other did not like having two large caves in his tank. Once I removed one of them to free up more swimming space, he stopped biting himself. It just takes some careful trial and error--try not to stress him out by changing a bunch of things around constantly.