Most of the above is great advice. Especially watch weather reports--that could kill the whole trip.
No cell service at HM. I get service on Sprint at Whitney Portal. Verizon works too. ATT down the road a ways.
I would definitely sleep at Horseshoe Meadows the first night. There are plenty of walk-in campsites (carry your bedding about 30 yards from the car). You don't need a tent, only a 20 degree bag and pad, on a trash bag for ground cover.) Or do like me: Arrive late, sleep IN the car! The place will be practically deserted.
Drive back down to Lone Pine to get that walk-in permit the day before the hike. Or watch the
on-line site for any cancelled/returned reservations in the week before. $15, but you can be more sure, and pick it two days before the hike.
I like taking a sleeping aid the first night as the first night on the ground is always difficult to stay asleep (I use otc Benadryl (Diphenhydramine), but try it once at home first.
You don't need to "camp". Just sleep on the ground, and eat out of an ice chest (kept in a bear box at parking lots.)
You don't
need to hike at altitude to acclimate. Just being there reading and resting will do. Acclimatization has more to do with your cellular structure getting used to the change in atmospheric pressure and oxygen level, I think. Remember those rest days before a marathon. Here's an easy acclimation hike if you want:
Trail Peak: Warmup / acclimatization hikeDiamox now comes in 125 mg tablets. I have that. With your strong sensitivity to AMS, I'd take half a tab twice a day, starting 24 hours before I arrive at HM.
With two days, you could camp at HM the first night, then either HM or maybe the Whitney Portal walk-in sites the night before the hike, get up early and start the hike.
Watch out for lack of sleep. Anything less than 5 hours for me, and I can feel nauseated the next day -- same as AMS symptoms.
Hiking too fast, lack of sleep, too little water -- all those things can help bring on AMS symptoms.
Have fun! I think you will make it this time.