This is getting really spendy, but for an extremely comfortable carbon flat bar road bike, you would be hard pressed to beat this:
Liscio / Flatbar / Shimano XT | Volagi Cycles

I have back problems too, and the Volagi design does a great job of keeping the road chatter out of the seat post.
Also these bikes are very flexible for tires size; for an extra soft ride you can get bigger tires all the way up to 47mm.