Morning Shell!
The only thing I have to offer is from my own experience. I find that if I sleep in my back, ...it allows the lower jaw to relax back down towards my neck. This puts pressure on the joint, and causes me more pain in the long run, ...so I sleep on my side if possible now.
However, with back problems, I do tend to still sleep on my back, with pillows under my knees from time to time. The splints used by the Dentist are probably the best way to go,...so I agree with Betsey Ross on this one. They can be expensive, and I'm guessing that Insurance will only pay so much on them.
TMJ can be miserable when it flairs up, so I feel for you! Stay away from crunchy foods and snacks if you can, and try different sleeping positions and see if that will help make a difference.
Take care,
SE