It sounds like you have had several discs rupture. With hardware in your back, you need to determine the right position for you. Like the others, I would (if I were you) go and try a number of bikes and positions. Realize that the LWB bikes may have a more upright sitting position than some others, and that with this type of back injury, you may need to be less vertical than is allowed on some bikes. When you sit vertically, or even semi-reclined (I have a Rans Stratus, and that is semi-reclined), the bike will absorb some of the vibrations, and the tires, and seat. But aside from that, most of these bikes will transmit the remainder of bumps, etc. onto you back directly. Some of the other bikes, including short wheel-based bikes (SWB) have active shock absorbing features. You should test these too.
Good luck,
John