I'll agree with the comments here for the most part. Dan M. Runs a top notch outfit and you would be well taken care of. I hunted the Alaska range with one of his guides and killed a great ram.
Alaska is cheeper that The Yukon or NWT because of competition. Those Canadan hunts can be $3-5000 more but have lots better success rate. Travel expenses are also more, $1-3,000 more. I do feel the experience is more relaxed though.
If possible research some possible outfitters, contact them and see if you could put a deposit down holding a price. Maybe this years or next years price. This works for me as it can save on raising costs and it farces me to save. Most outfits will be willing but 3 years out is max I've found.
For me I budget:
Airfare/hotel $1-2,000
Tip $1-1500
Extra $1,000 (gifts, alcohol, dinners, baggage, ect)
Taxidermy $1,500- $3,000 (life size or shoulder mt)
Hunt cost - right now I think $20,000 is probably average.
If your serious about a white sheep, id look to find as many raffles to enter as you can afford. Most WSF chapters and National WSF <1 club program has fully guided sheep raffles. Washington WSF will be giving one away, we just did 2 in march(dall, stone) as a door prize next year.