I have had that especially after I hurt my back (not broken). I found that putting my tank a bit lower, occasionally bringing my knees up to stretch my back whether vertical or horizontal, changing fin techniques on and off - scissor, frog, during the dive, being in better shape by strengthening my leg and stomach muscles to take the stress off back muscles, to just relax and not clench back muscles during the dive and to take various trim positions during the dive. At times if necessary I will pull the tank to one side during the dive for a bit. I will also take a lotus position during the safety stop to stretch my back. If I keep the exact same postion - head, neck, feet, and diving for 60-80 minutes, my back will hurt. Keeping a head up position for a long time will also cause the "U". I dip my head quite a bit as matter of habit.
Most of what I am saying is, I don't keep the same position for long periods of time.
Some dives I don't have to do any of this but others I do. I have found that if I have been sitting alot, before and during diving days, my back hurts more.
If you have floaty feet, maybe consider ankle weights. I don't use them.
If you broke your back, I assume you have some physical therapy regimen to follow. I can say for me that the physical therapy/excercise was better than any other treatment I was given. My back hurt for months after injury and still does at times after years. Expecting no pain after 6 weeks may be a bit much to ask but YMMV.