Norcal: I wouldn't blame your dizziness on Diamox, unless you took way too much. (125 mg twice a day is the max I have seen advised for altitude.) It is more likely a result of your body's reaction to the altitude and pack weight.
I wouldn't aim for November. Last year, the first snows hit the end of September. It will be cold and days are quite short, making for many hours of darkness.
The walk-in permit option is far better. Check the
Unused Whitney Permits 2010 page. You can see for overnights, from August 23 on, there was always at least one overnight permit available except for 4 dates.
And those numbers are after ALL walk-ins ALL day long were satisfied. If you are there at 11 a.m. when they make the no-shows available, you have even better chances.