Revised theory : The gagging coughs I was experiencing during the height of the sinus infection did physical damage, so I am not waiting for inflammation to subside, I am waiting for damage to heal. Got an ENT follow-up tomorrow.
Better ENT visit. He was able to use mirrors to actually get a look at the voice box, suggested that I should give it another two months, and if I hadn’t gotten back to where I want to be, come back to him and talk about some other options.