Holydiver, please don't give up. I have the EXACT pain as you do. Mine started suddenly before Thanksgiving this year. It feels like my gums, the roof of my mouth, and my tongue are one fire constantly. It also feels like whatever it is it's trying to push out all of my teeth.
I went to see my oral surgeon who took a simple x-ray. He didn't see much, but he thought he saw some infection in a bone graft I had above tooth #13. He requested my PCP to order a CT scan stat. I got the results last week, only to find out no infection was detected. I was truly discouraged, however, it did detect a small mass of some sort in that area. My PCP then ordered some very specific tests for infection. Those test results came back today - no infection.
In the meantime, I've had to have two IV drips due to severe dehydration from all the antibiotics and pain medication.
I see my OS again next week, but he called me in the meantime and suggested that it might be maxillary cancer, which is very rare. I am hoping and assuming you have been tested for a bone infection or cancer. Bone infections in this area are hard to detect with a CT.
When I read your first post I was moved by the fact that you described my pain exactly. My heart is heavy for you and hope we both get a diagnosis soon.