Wow, those are some mighty joint issues! And I could see some of those making yoga pretty difficult. I don't know a whole lot about it, but perhaps Tai-Chi might be a better match for you? I understand it has some of the same mind-body connection aspects, but it definitely has less emphasis on the thing that sound like they would hurt you.

I could actually do most of my yoga without a mat, there are just a few poses where bone presses directly against the floor, in which case I would want a mat. But, in general, I am pretty "well padded". *grin*