You say you have back problems. I broke my back in 1986; needless to say I look at all bicycles from the perspective of back comfort.
Something a little out of the ordinary to consider is the RANS Fusion, or if it is a little too pricey, the Electra Townie. The RANS bikes are beautiful high end bikes with nice components from a top manufacturer of recumbents. The Electra Townies are suprisingly nice bikes. They use something called a Crank Forward design. It's not a recumbent, you don't sit back, there is no seat back. You do sit lower in the bike by a bit than on a standard diamond frame, and you can flat foot the bike.
The beauty of the crank forward bikes is that you don't stress your back, not at all. You do feel some pressure on your arms, and you definitely use your core muscles so you feel it a bit in the stomach. On the first couple of rides you might feel a bit of stress on the lower back. But once you acclimate the back pain is gone. RANS makes some very light high end crank forward bikes as well.
I searched and searched. I tried everything, putting on a higher stem, using a hybrid, using a suspension fork, various handlebars, various seating positions. Some of the things I tried worked to some effect to keep the pain manageable. The Crank Forward design meant no pain at all. Check out
www.ransbikes.com and
www.crankforward.com and
www.spincyclz.com.