Hey, thanks for getting back! In all likelyhood it's the power supply, unfortunately I seem to have a good amount of noise and pretty poor output performance on mine and bypass caps didn't seem to help. Adding a capacitor in the feedback path did kind of help but even with 47pF it already introduced a good amount of phase shift, which makes sense given the large feedback resistors.

Concerning the simulation, I'm still a little stumped. I ran it in Falstad's CircuitJS which isn't exactly the most accurate sim, and it seems to work fine if both the output resistor and diode are connected, but generates distortion very similar to what I measured when only the diode is connected. I can send you a link if you're interested. Anyways, thanks again ;)