> I should have a very good chance of securing a permit if I try on Monday and Tuesday if needed?
Yes, very good chance. Not sure when your ride Sunday will be over, but you could go in before the 5 PM closing and inquire about a Monday permit. Some may still be available.
> I assume the times given with regard to securing a permit are for the previous day, right? E.g. 11am on a Sunday to get a permit to hike on a Monday?
I believe you intend to DAY hike, right? If that is the case, the no-shows become available at 2 pm, not 11 am. Note that I recently updated step 6
in Wilderness Permit Options to reflect the correct 2 pm time. Some permits come available before the no-show time, too.
> any thoughts as to how this might serve for acclimatization?
With the several hours spent climbing to HM and WP, you will have some
acclimatization, but not likely enough. Being very fit is sometimes a disadvantage -- gets you higher faster so AMS can come on faster. If it were me, I'd get an Rx for Diamox (Acetazolamide), NOT the 250 or 500 mg, but 125 mg low-dose. I'd try one at home to make sure it doesn't bother you (if it does, try half the 125 mg). With that Rx, take one the night before, and one the morning of your hike. It may well help. ...or go without, be aware of headache and nausea symptoms, and turn around if they come on too strong. Make sure you drink lots so you are peeing every couple of hours, and snack a lot, especially lower down, in case you lose your appetite higher up.
Also, once you get your permit for next day, if you have time, drive back up to HM, and sit around and read a book for some hours. It will be time well-spent.
Good luck on the bike race!!