For a completely different take on back pain and the solution: I've been riding fix gears as winter/city/rain bikes forever. Always used road frames. The components just go from one frame to the next. (Those bikes used to live hard lives, Bad things happened to the frames.). Setup #4 was a large touring Miyata with a very long/high headset and shortish top tube. I slammed the 13cm Cinelli 1A stem. The first 5 years I suffered up hill. Couldn't breath deeply causing anaerobic pain early in rides and my lower back really wasn't happy. So I took a wild gamble. I had a local framebuilder make me a 180ch stem. An early ride with that stem was 75miles and some real hills. Hard! Tiring! No back pain!

I am aging and my stems are coming up and back, but slowly. 20 years and many bikes and stems later, my stems are 175cm -5 degree, 155cm -5 degree, 135 Cinelli 1A near slammed on a short head tube frame, 130 Nitto Pearl (140 in anybody else's book) on a long top tube custom and a 120 -17 on another long top tube custom. My back and body love all these bikes.

Edit: I forgot the mantra I came up with when I went to that first 180 stem. The cat stretch. Ever watch a cat do the stretch were it makes it's back really long with a bit of sag? I don't actually do that, but my back can relate.

Ben