The big difference between modern geared bikes and single-speed/fix gear bikes is the virtually all geared bikes now use vertical dropouts for the rear wheel. SS/FG bikes have horizontal slots to put the wheel into so you can easily slide the wheel forward and back to adjust the chain slack for different cog sizes. With a bike like your current one, there are very few choices of chainring-cog combinations that work with the proper chain slack. (There are 1/2 links so it is possible to make 1/2" chain length adjustments, not full inches, so that helps a little. Still, very limiting.)

With a flip-flop hub and a SS/FG specific frame, you can make real changes in gear ratio and make up the size difference with the long horizontal slot (either a track end, a true horizontal slot that opens to the rear or traditional horizontal dropouts that aren't quite horizontal and open to the front - on all geared bikes 50 years ago).

DiabloScott nailed it as to how you can adopt your current bike and the limitations. With what I said above, you can see why. If you plan to do a lot of flipping, track ends are a little miserable because you have to slide the wheel forward to get the chain off the cog and reverse to get the wheel back on. Horizontal road dropouts are a lot easier. You slide the wheel forward to remove anyway. Drawbacks are 2 - horizontal dropout exist almost entirely on older pre 1990 bikes and they are a lot shorter than track ends and limit your gear choices (unless you custom as I did).

And on your other subject - your back. I have back issues -lumbar and tailbone. My back loves climbing fix gear. The best possible stretch! I won't claim this will help anyone else but the hard pulls required to go up real hills in huge gears are like PT I would have to pay real money for. Oh, and while I am here - if you want to to that kind of climbing, you have to have your shoes secured to the pedals (toeclips and straps, clipless and a few other options. I use toeclips, straps and the slotted cleats racers used 40 years ago.

Ben