I agree with using Equine Senior until you can get him over this inflammatory event. It is an excellent complete feed that would not irritate or cause him to open his mouth very far. Corn oil is also good for calories from fat.
I also think a sedation and mouth exam is in order.
Since this was first posted, do you have any more information / lab work? Is your veterinarian treating for anything specific, or still having good success with general treatments?
There are a couple of other possibilities on your horse. Number one is a reaction to something in the hay or pasture such as a weed that is irritating the gingiva or a type of grass like spear grass. Since your horse is 85% better on Banamine only, I would think this may be possible. Consider trying a new hay. Also, there is an unusual condition that involves inflammation of the cementum of the teeth that affects the incisors. It causes inflammation of the outside of the teeth and gums but usually does not clear up with banamine but usually required steroids and sometimes extraction of teeth. However, usually the x-rays of these teeth are abnormal. As far as opening the mouth, this could be pain or inflammation in the muscles of the jaw. I would consider sedation and finding out if the can open the jaw or just does not want to do so. If it is impossible to open the jaw, consider a muscle problem that is usually immune mediated but rare.
All that said, I suspect your horse reacted to something in the hay or pasture and the mouth is still sore. As far as loosing weight and not eating hay, consider feeding a complete feed like equine senior so he will not need hay until the soreness decreases. Also, your vet can biopsy the inflamed tissue to maybe get a better idea of the cause. If he still needs to gain weight, ask your vet about adding corn oil to the ration to increase calories.