So I have some work to do porting the OpenCL kernels from bullet3 to work on ATI cards in Ubuntu before more progress can be made implementing the plan Steven Peters outlined above, at least on my particular setup. I'll report back when I get this working.
Bullet3 is now working fine on my old HD 6900 ATI, so I decided it was time to follow Steven Peters suggestion and increment the minimum required bullet version to 2.83.
It appears to be working after I made a couple of minor edits. I can make a pull request if anyone else wants to see what I have changed so far. I'm pretty sure I haven't begun to scratch the surface of the changes that need to be made to fully utilize the GPU computing capability of Bullet3, but first things first, Gazebo works with bullet-2.8.3.