My 10-year old son has constant abdominal pain and we are completely at a loss

My 10-year old son (normal weight) has celiac disease and we've been gluten-free for a few years now. He's had severe and constant abdominal pain for 2-3 years and the past few months it's been getting worse. He often can't walk, and he's missed months of school because of the pain.

The diagnosis is that his brain is somehow over-processing the pain that normal brains just ignore. There is no inflammation or physically-detectable clues. The pain is especially intense at night, and the second he wakes up the pain is there again. There is no reprieve throughout the day.

Doctors have had him psychologically evaluated, tested for autism, and had a social worker visit us occasionally to monitor our domestic situation. We're just a normal family. He's bright and well-adjusted, and gets hugs 100 times a day. No visible causes or signs of anxiety. The pain is really bad, though. He is in utter despair and has talked a few times about just stabbing himself and ending it all. Edit: I should add that he has a lot of nausea, and often says that he feels "odd" or fears that he's going to die from the pain.

He had an esophagogastroduodenoscopy done last week and his stomach and duodenum are fine; the pain is around his navel area.

We've tried to eliminate all kinds of food, but there's no change.

I'll be really happy for just any suggestion or idea.

Edit: Thank you so much for all the comments so far! I managed to get some great info. My apologies if I don't respond to your comment, but I do appreciate it!