I'll just throw my oar in here in case it helps. I have had bilateral OD, and was taking methimazole when I had that surgery, as well as the strabismus surgery. In fact, my FT3 was a little elevated for the last surgery, but the surgeon and anesthesiologist said it was OK to proceed. My PCP said the main purpose of the pre-op these days is to check that our hearts can tolerate the surgery, and of course, you're monitored very closely during the surgery.
I had gotten in my head from somewhere that maybe if I waited long enough, since my optic nerve wasn't compressed, that my eyes would improve enough to avoid the OD. My surgeon said I could wait as long as I wanted as long my eye health wasn't further compromised, and I might see some improvement, but it wouldn't be enough to avoid the surgery. My PCP and endo agreed, as did the strabismus MD. At any rate, my husband reassured me that the surgeon, who was voted a Best Doctor by his peers, wouldn't make a recommendation that wasn't sound and put his reputation at risk. Made sense, so I took a leap of faith and agreed to it. I have to say, I'm glad I didn't postpone it further.
Also, I was off of methimazole from last May until February. I'd hoped I was headed toward remission, but my TSH just never came back up. (Sadly, everything but my TSH rose…) So I've had a little hyper-blip, but I felt better within a few weeks, thank goodness, with just a little bit of methimazole, which I am still taking. Anyway, hope this helps.