There must be a good LBS that has experience with this, so keep checking. Ask them about doing a pro fit. The pro fit might well cost some dough ($50+) but it is well worth it.

The upright position of comfort bikes is actually worse for your back than bending over the bike, as long as you have proper position and fit. Think about it: going over bumps in the upright position sends the bumps right up your spine. In a bent-over-the-bike position, the shocks are absorbed by your legs and arms (remember to ride with your elbows bent and supple).

Other than that, many back problems, especially lower back, are worsened by poor posture and weak abdominal muscles. Strengthen your abs (correctly--form is very important) and that will help. If you can take a yoga class, that would be very helpful, too. A supple and strong spine is a delightful thing to have.