Just an update for anyone experiencing similar issues:
Turns out my Wifi router was too close to my PC and causing interference with the motherboards Bluetooth. I bought a USB Bluetooth adapter that was advertised as a bit more robust in terms of signal and turned off my motherboards built in Bluetooth. This has resolved the issue for me. Good luck!
I have been fighting with my headphones for the past 2 years, ever since I got a new pc with built-in bluetooth. They worked just fine with an audio cord, but would only ever see LE-Bose as the only bluetooth source, and even then fail to connect. The headphones seemed to arbitrarily work sometimes, but never well. I resorted to getting a usb dongle, which didn't result in acceptable audio quality. Every few months I'd try again, going down rabbit holes of reinstalling drivers, installing 3rd party drivers, system updates, reinstalls, registry editing...all to no avail. Countless hours over the past 2 years, completely stumped. This comment right here was what sent me on the short path to finally figuring it out. It turns out in building my pc, I hadn't connected the antenna to the bluetooth adapter.
What I was convinced was a bluetooth driver issue was actually a hardware issue, and I would not have been able to figure it out without this comment. It may not have been the same pair of headphones, or even the same problem, but I nonetheless wanted to go out of my way to make my first support forum post to say thank you. Thank you for putting an end to years of pain and heartache.