> We will have been at higher altitude, but not camping at high altitude for the previous 3 days
Your susceptibility to AMS partly depends on how many hours in the previous 3 days will you be above ~8k. Sleeping at altitude would help a lot. I always take half a 125 mg Diamox 2 times a day starting the day before hiking that high. It's a low dose, but can help.
I always hike with two hiking poles. Used to scorn them, but that was when I was younger.
Water: you only need a liter each until you leave the Cottonwood Lakes. Drink lots, half a pint to a pint per hour. Refill when you run out at the many water crossings. You won't need water shoes.
Good luck, have fun!
