I'm feeling fortunate that my experiment didn't hurt my shoulders. Overhead pulling, like pull-ups, does produce this horrible clunking sound in my left shoulder as my hands/arms return to normal position, but it doesn't hurt. My shoulders are so much better now that I work them more. I have been assigned many physical therapy exercises for them but this is the one that helps most: http://www.youtube.com/watch?v=12i9VmaIpx0 with some modifications. I use 3-lb dumbbells, never anything heavier. I do the Y, then the T, then the T with my hands rotated (so, palms just turn about 180). The W portion I do on an incline bench, one arm at a time and I use more weight (because I can). So when I'm experiencing shoulder pain in general everyday life, I add this exercise back in whenever I'm doing upper body work in the gym, usually in between my first and second circuit so I'm warm but not too tired.

I will investigate push-up bars for regular push-ups. Maybe they would make burpees less excruciating (they bother my back)?