You could always go for a larger, longer tank like a bookshelf 6.6 gallon, but with a much reduced water level. He can wiggle up and down that and still be able to surface for air in the low water.. and it'd be somewhat less a hassle than changing his current tiny tank daily to avoid ammonia issues.
If you got a mini-heater (I use the 30w Dymax ones, they're small, reliable and powerful enough for a betta tank) you could position it on or near the bottom of the tank so as to heat the water properly.
You could add lots of plants and floating wisteria, stuff to help him prop himself up for a rest near the surface and hide in to feel more secure. And do partial water changes with pre-aged/tanniny water a little bit warmed by a couple of seconds in the microwave, or just use warm tap water, and leave him in the tank meanwhile.
Less stress for you, less for the fish. The IAL is a really good call for stress reduction/injury treatment as well.
I'm really curious as to how he got his fins ripped off!