As a fellow "teeth clencher, morning headache and terrible jaw pain" sufferer, I can really relate to what a drag it is to get up in the morning.
I believe my teeth clenching is due to stress rather than my AD as it began long after I started the antidepressant. Perhaps, for you, changing meds will help.
I also tried the mouth guards you can purchase in pharmacies, but it wasn't until my dentist made me one specifically for my teeth that I got real results.
I have mild TMJ which is exascerbated by arthritis, but the mouth guard should hopefully slow down any more wear and tear on the joint.
I would recommend a discussion with your dentist about your options.