Sorry for the double post - just wanted to give a progress update.
I spoke to my optometrist again regarding the patching + suppression theory:
-I explained that no patch is a 10/10 (1 being no symptoms, 10 being the worst) for symptoms from a flickering screen. Wearing a patch on the right eye reduces symptoms to 4/10. Wearing a patch just so that it covers the flicker but allows for peripheral vision is more like a 7/10. He very cautiously said this could indicate an issue with binocular vision, since I experienced more relief by completely shutting the eye off with the patch. He said something to the effect of "There's nothing factually wrong with what you said. It makes logical sense, but I can't make any medical determinations. It's possible that the right pair of glasses could address the BVD and help with the flicker issue, but I'm not sure how likely it is". I was referred to a BVD specialist and will be seeing them soon.
-I also explained the eye suppression theory, where we may potentially have a suppressed eye that is being "woken up" by flickering screens. He didn't seem very receptive to this theory, though. I'm seeing him in person soon, so I'll try to get more info on this.
In my opinion, I think it would be really helpful to see everyone else's results with the half-patch test. Basically, if normal usage of flickering screens causes you a 10/10 for symptoms, try wearing a patch and figure out which eye provides the most relief from symptoms. Then, once you have that, try the half-patch method and see if you get the same relief as the full patch. What I did is curve the patch so that my right eye had zero exposure to the flicker, but I could still see with peripheral vision. This should keep binocular fusion intact, and potentially indicate if BVD is the issue, not just flicker exposure.
Here's a terrible quality mockup I made to show how it looks, lol.
Basically, you just want to cut off one eye from seeing any flicker, while still being able to see the peripheral. If a ton of people have the same experience as I do (The half patch not giving as much relief as the full patch), we may have an actual lead to go on here with BVD or something similar.