do they think you can do some training to maybe lessen the gag reflex or train yourself to be less sensitive. Like meditation exercises that teach painful recovery folks how to relax and let go??? maybe this isnt possible, maybe it is. Can they cut the plate of the denture so that it doesnt ride so far back on the palate? Have you considered implants in the back, and a partial in the front? the implants are expensive but if you popped a couple in the back, they would provide the anchor for the partial. Or perhaps implants all around if you can afford it.
Call a dental school (even if you dont live near by) and ask what are the latest things happening for folks with your condition. You cant be the only one.
I hope you find answers.