I think you should talk with a PT who has experience with cyclists. None of us can really tell you exactly where the issues are with your back, and what might aggravate it.

I will say that my friend who had back surgery a couple of years ago, was able to return to a deeper tuck. He'd had to ride with a tall stem stack and relaxed geometry before surgery, but after he'd reached recovery, he was able to get a new bike with his preferred riding position.