Meanwhile, the orthopedist I had seen for my shoulder suggested I try to correct the hunch I've developed from sitting at desks so that my shoulder doesn't heal in an awkward position. I had been doing that and noticed that every once in a while, I would sleep perfectly fine and wake up fully rested. This made me suspect this was a fixable problem and not some permanent feature of my anatomy.
After ~6 months of exercising and stretching to fix my shoulder hunch, I could finally sleep through a night and today I get better sleep than I can remember having in many years, without the CPAP. If you think you have sleep apnea, I'd recommend checking out r/posture on Reddit to see if you might have poor posture first. It can be really difficult and uncomfortable to fix if it's been developing for ~10-15 years like mine, but it's so worth it and there are a lot of other nice health benefits that come with it.