I agree with Richard Glover. Back problems are no reason to avoid drop bars. Flat bars end up in the same place as the tops of drop handlebars. The only difference is that now you only have one hand position, instead of the multiple positions offered by drop bars. I have neck problems, and I find that forcing myself into one position for long periods of time exacerbates those troubles. Being able to move around a bit really helps. And of course, you have already discovered that flat bars limit your choice of shifters, as you have discovered.