If you were a client of mine, I would suggest looking into recumbent bicycles.
You would be able to maintain an almost neutral pelvis on a recumbent. Also, you would be pushing against the back of the seat rather than using your body weight to pedal. This would substantially decrease strain on your lower back while keeping your body aligned how you need to be. Your sits-bones would be more cradled while possible saddle-chafing would be reduced.
I think you're a prime customer for a recumbent. Sadly, they do tend to be pricier...but what good is an inexpensive bicycle if it's only going to hurt you?