Bench Rest matches are held regularly at the Kenmore Range and they have several different classes. The "Factory Class" is great for someone who doesn't want to invest thousands in a rifle that just sits there and does all the work but "pinching" the trigger.
There are several people who show up with similar circumstances. I had a leg crushed many years ago and can't kneel. When I shoot prone I shoot for a long time in that position so I don't have to get up right away :) The Benches are designed with a lot of leg room so it may be of interest to you.
http://www.wcwinc.org/Each range is fully handicap accessible.