I too have EDS and TMJ. I used to work with at physical therapist who treated TMJ. All of her patients loved her and talked about how great the treatment was and how much it helped. My TMJ was just developing at the time so I was never treated by her. Maybe PT could help though. They may be able to offer some exercises to improve stability or some form of treatment to help with the pain.
I have had severe headaches for years but I don't think it's TMJ related. I found a trigger for my headaches to be strawberries and have dramatically cut the number of headaches since I quit eating strawberries.
I use heat on my jaw when it gets really bad. That seems to help with some of the pressure and cuts down on a little bit of the popping but it doesn't last long enough - luckily for me my jaw pain is one of the least of my worries though. My hips and other joints give me more trouble than my jaw. I find that if I stretch my jaw and make it pop (like popping a knuckle eases the strain in the finger joints) that helps sometimes.
I also was put in traction for my neck (I have fused verterbrae in my neck) and that seemed to really help with the headaches and jaw pain. Sometimes I can pop my neck and that will help as much as the traction did.
Those are the only things I know of to do except for pain medication and there you could try something like Ultram that's non-narcotic maybe? Or an anti-inflammatory if you can tolerate them? I would ask your dentist if he has any advice or if he could send you to a TMJ specialist to get some ideas. I'd stick with the same dentist but maybe get a little added help from another dentist/doctor/physical therapist/? whoever the docs/dentists recommend for you.
Hope you get some relief soon. Take care and God Bless you.