I have had no trouble getting prescriptions for Diamox, but my husband had a doctor who said “no, it’s a glaucoma medicine and I won’t prescribe it.” We shared my prescription. The second time I used it, I stopped using it after a couple of days because it is a diuretic and I was peeing every 10 minutes. The headache was easier to handle. Altitude sickness can slow you down a lot though, especially if it keeps you from sleeping and eating.
One thought, if you only have three weeks, rather than attempt to hike 20 miles a day to do the whole thing, why don’t you start at the southern end and just hike as far as you can. That way, if you get caught up in weather or have problems with the altitude you can take your time. The southern part is the best part anyway.
Another thought - don’t count on the storms being only in the afternoon. We had several days of all day rain – including total whiteouts that made navigation really iffy. With two people, it wasn’t so bad - one would stand at a cairn, while the other would head forward, looking for the next one. When they found it, they would shout, and the other would move forward. That way we were more likely to actually stay on the trail, instead of getting completely off track. (Of course, there have been a couple of times when we were following cairns that way through a whiteout, and they turned out to be the wrong trail. Ours branched off and we missed the turn because we couldn’t see it.) My point is, weather may slow you down more than you expect. You could even get snowed on at the end of August.
Ginny