I have a USE Shokpost on my hardtail MTB and find it good for absorbing moderate hits. I usually watch where I'm going and use my arms and legs as suspension by raising myself out of the saddle before the bike hits an obstacle but the suspension post is good for when I hit something unexpectedly. I think it might be quite good for you with your back problems.
You can get shims to allow the post to fit different size seat tubes and can change the internal spring and damper for different body weights.
Potential problems? The post doesn't have 'setback' like a normal road post so you might not be able to get your saddle back far enough (you'd have to try one to see). After a lot of use, the post can develop some play but you can replace the worn parts. I haven't bothered on my MTB. I've got a few mm rotational play now in the saddle but it doesn't affect my riding or comfort.
If you get one of these posts, remember that your saddle will be have to be set higher than you currently have it to allow for compression of the suspension when your weight is on the saddle. You have to get used to this because it means that the nose of the saddle can snag your shorts when you are mounting the bike unless you lift yourself higher and drop yourself down on the saddle. You soon get used to doing that.
I used to have one ( a suspension seat post) on my hybrid I changed it to a fixed mainly because I wanted extra space for lighting brackets but also because on an older bike I found that it was causing me knee problems. I think the travel up and down meant my leg to pedal varied slightly, this may have been the result of a cheap seat post though.