I've no back problems, but to give you some idea on the effects of a rear suspended recumbent, if I ride 20 miles on my road bike, my 47 yr old back will feel it the next day. If I ride 35 on rear suspended bent, not a hint of strain.
Rather than visitting a general LBS, I'd visit recumbent specialty shops or manufacturers in your area. You have many in the Denver area, some of which have already been identified. Most general local bicycle shops are clueless on recumbent specific issues, even shops that carrying a recumbent or two. Many general shops will try and limit options to either the bent they have or steer you away from recumbents even if that is the route you ought be going. A recumbent specialty shop will have several models for you to try, will be accostomed to seeing customers with chronic back problems and have a general idea on which bents might work well with your back.
I'd recommend suspension to help with the jolts on the back.
Recumbents are fun independent of medical problems.