Just an update: I purchased the BenQ TK700STi gaming projector (a DLP 4K projector), which uses a lamp bulb as the light source. Since this has no LEDs involved, I figured it wouldn't be a problem- but I was definitely mistaken- this projector definitely caused my eye strain symptoms as well! Since this projector uses pixel shifting to accomplish 4K resolution (like almost all 4K projectors), and since it's DLP (flashing red/ blue/ green can be seen with eye movement), I am now back to strongly suspecting my main issue, like many of us here, is dithering or flickering. (I know PWM doesn't personally bother me as my main tolerable 10 year old monitor uses PWM, but some type of pixel dithering or perhaps even light source flicker itself must be my main problem!)
So, despite my disappointment the BenQ TK700STi projector didn't work out, at least this is helping me narrow down the problem. Despite being so widely thwarted (I've tried something like 32 monitors now!), the hunt optimistically continues!