I apologize if I repeat or misunderstand.. this is a long post and I only skimmed it.
He is looking much better. The white stuff on his head is still there but it looks like it is almost gone. It looks like a slime coat infection. It is not ich. You do not want high temperatures for this kind of infection... Lower the temp to 78-80* for now (bacteria like warm temps). If it doesn't go away after a few more days you should consider treating him with Aquarium Salt.
I'm not sure if anyone mentioned this, but tap water is much healthier than bottled water. If you condition the tap water with API Stress Coat it will also help him recover from his infection.
You are doing a great job with him, he looks like a completely different betta!