An update on my situation:
tldr: Still doing well with the patch, hopefully seeing a neuro-opthalmologist to get answers to the questions
-Been using the eyepatch on my right eye , ~4-5 hours max usage per day. Still experiencing reduced symptoms while & and after wearing the patch, and I haven't had any negative side effects aside from the normal slight strain that comes from using just one eye.
-Spoke with my opthalmologist, I'm hopefully getting a referral to a Neuro-opthalmologist where I can explore the potential BVD/convergence issue further.
-I tried a different test with the eyepatch based on Mike's suggestion. I had the eyepatch set up so it covered half of the right eye, so only my left eye could see the screen + flicker. The right eye could only see the peripheral view, if that makes sense. This made it so I was only getting exposure to flicker with one eye, but not breaking binocular fusion. I noticed that I didn't have the same level of symptom relief as when I fully covered the eye, meaning that my issue could potentially be related to binocular fusion. I'll be asking the doctor about this as well.
-I bought a Brock String and have been messing around with it. I don't have any issues with the exercises, and I'm able to keep each bead in focus with no problems. Not sure if I should keep using it.
-I'm still very hopeful that pursuing the BVD issue will lead to some kind of explanation for our symptoms, I'll post back here if I learn anything new that may help