I had the same problems until I did the following:
1. added a heated humidifier. DME originally set me up without it. Makes a huge difference
2. Went to the Mirage swift. Not perfect since I too am a belly/side sleeper, but better than the traditional masks for my claustrophobia. I learned how to position the hose, adjust the mask, etc., so I could avoid leaks most of the time
3. PRACTICE. In the afternoons, evening, whenever (but not bed time) I would put the mask and CPAP on while watching TV, working on the computer, or whatever other stationary tasks I had. It helped me learn to just breath with the machine on, and not focus on the machine. Once I was comfortable with that, I transitioned to using the machine for my afternoon nap or would fall asleep on the couch with it while watching TV. Again, this was all out of the bed, so I didn't have the desire to roll over on my side or belly.
These steps made a big difference for me, but I still found myself taking the mask off at night in my sleep without realizing it. I just switched to a cflex unit with the breeze nasal pillow system. Seems to tangle less and leak less than the Swift, although I don't find it as comfortable. hopefully this will do the trick for me.
I hope these tips help you!