I really like the answer from sheephunteralaska...but another option and opinion-Save up your money and do the Canadian route, especially the Yukon and NWT. Some I've hunted with noted below-
Dickson Family is topnotch...couldn't find a nicer multi-generational outfitting family; Mervyn's Outfitting also topnotch; Dan Reynolds will be booked four years out...if you can get on his list, he's the best outfitter in Canada especially for the age of rams and size/age of moose. He also won this year's Short Take Off/Landing at the fly-in in Valdez...I believe he set a new world-record; Gana River and Harold Grinde is topnotch...best stock and gear is first rate...Harold is almost too honest for his own good-a compliment!; now that Griz Turner (from Wyoming's Lost Creek Outfitters many years...a great elk, mulie, and RMBS outfitter) has taken over Dave and Dallas Dutchik's concession and Redstone is now called "Raven's Throat"...the concession hadn't been hunted near as much as the limited draw areas in Alaska. There will be some OLD rams coming out of Raven's Throat next few years...Speaking of Alaska, the Ultima Thule area borders the Kluane First Nations area across the border in the Yukon...great family and superb area. Back to the Yukon, if you're in tip top shape, Chris McKinnon's Bonnet Plume area is also underhunted and has excellent genetics for mass. Jim Fink of Blackstone does a decent job, adjoins Reynolds, and punches 3x the sheep tags that Dan does on his side of the line...I've been in the office in Dawson City within an hour of their guides buying up the available licenses, leaving just two (exactly) for myself and another hunter for Dan/us in person, to purchase, otherwise we would have had to wait and lose hunting days...now they still do a very good job, but I've had very experienced sheep hunters (at least two who were sheep guides themselves here in the USA) hunt hard at Blackstone and not see any rams over 7-8 years old and no longer than 35"...not a blanket "no" but make sure you do research as to how many hunters come in every year, the average age/lengths of rams, etc...the information you can get from the AK and the Yukon biologists, either via internet or start an email inquiry.
I've hunted AK and the Canadian side. If you're working hard and want to make sure you've got the area/concession pretty much to yourself, you will pay more, but overall you're experience and the age/amount of rams...as long as you're in "Sheep Shape"...will be a much more memorable experience on the Canadian side. Of course if you get the limited draw tag in the Chugach or TMA...it may take half a lifetime as a non-resident to draw the trophy/limited areas.
No disrespect was meant to anyone and I apologize if I left out some of the others that I've not hunted with: the Lancasters are a fine family; South Nahanni I'm not familiar with, both have excellent reputations.
Just my two cents,
Diddywahdiddy