Based on some online anecdotal evidence, I decided to try nicotine "therapy". I bought 4mg smoking cessation mints, cut them in half with a pill cutter, and took 10-12 2mg doses per day at roughly one hour intervals. The effect was immediate and brain fog lifted in less than a week. It was like coming out of a long dream, or like I had been stoned for six months and then suddenly I was sober again. My fitness stats have exceeded where I was before I got sick.
This is just my own anecdotal experience, and there have definitely been some downsides. The mints are about $50/month. My dosage has ticked up a bit and I'm certainly addicted, at least once a day I take a full mint instead of a half for an extra kick. I'd like to taper off, but I'm not sure if I do how to know if any effects are withdrawal or resumption of the covid brain fog. I have a light caffeine habit (2 cups every morning) and I don't see the mints being any more harmful than the coffee, so I think I'm just going to stick with it.