Awesome place for sure! You will love this hunt!
I was up there in 2012 the last part of August and first part of September - 12 day horseback hunt. Bowhunted for sheep and caribou. We got one full day of rain and a couple of dustings of snow. The weather was not too bad though and most days were very nice and sunny.
The merino base layers were awesome on my hunt - I had Minus 33 and First Lite. I had the First Lite Kanab pants that were awesome as well - really light for hiking and dried fast. I also took Sitka pants, vest and shell along, but they did not do as well as the wool and didn't wear them much after the first couple of days.
The Attack pants are pretty good and I have been using them for mountain hunting quite a bit and they are great for ventilation when you are hiking around a lot. The Alpine is awesome with the padded knees! Necessary for bowhunting when you might be squatted down in the rocks for hours waiting on that animal to stand up for the shot. Could be a help when rifle hunting as well if you need to get into a kneeling position for the shot.
Have recently gotten the superdown puffy from Kuiu and love it for backpacking- super light weight, packs super small, and is very warm... however it is noisy! Not going to be much use for bowhunting during a stalk for sure! I would definitely take the puffy and the pants and keep them in your pack!
You might want to wear that guide jacket on the plane - it will be handy to have along. A good warm vest will be great to have along as well - I took a King of the Mountain vest, but would probably opt for something a bit lighter weight next time.
You will want to have some really good rain gear. If you are going on horseback, it will need to be tougher as the horses will tend to scrape you up against the trees and can tear even the best materials.
Limit yourself to one set of merino wool base layers, one good pair of hunting pants, a vest, the puffy top and bottom, one good set of rain gear, a good hat and 3 pairs of good wool socks. You should probably take an extra pair of good boots for when you get one pair soaked (it will happen).
Good Luck!