Berryblaster,
One thing I find is the amount of mis-information floating around about drawing a bighorn sheep tag. I know you said you didn't want to wait 20 years, but the statistical reality is you could apply your entire lifetime for a bighorn in the Western states and never draw a tag. I don't want to sound gloomy, but the chances of drawing of Bighorn sheep tag anywhere are VERY, very low (did I say very, very, very?).
Montana: is the cheapest non-resident state with the highest quality rams. Unfortunately this creates some of the poorest drawing odds. The point system is cheap ($25/yr), but they really aren't worth much because they aren't squared and there are SO many people applying for the very limited tags. Also remember that there is no set aside non-resident tags, and non-residents may draw op to 10% of the quota per region.
Idaho: For some reason the myth that gets perpetuated is that Idaho has good draw odds for sheep. Nothing could be further from the truth. Like Montana, there are no set aside non-resident sheep tags, and non-residents may draw up to 10% of the total quota. Both Caifornia and Rocky's are available. Every year there are typically 5 non-residents that draw a sheep tag with about 850 people applying.(good luck in trying to apply for an area that will actually have a non-resident tag drawn). This equates to less than 1% draw odds with a very high application cost - $154.75 non-refundable license.
New Mexico: High cost up-front to apply ($3006), but low application fee and no hunting license to purchase. There is no point system in place, and all applicants go into the same pool (no non-resident quota).
Colorado: Has both preference points and weighted points in its drawing. A person must have 3 preference points to be eligible to draw a tag. There are tags reserved for non-residents with both archery and rifle tags available. Colorado is the state that provides the non-resident with the best odds of drawing a sheep tag (of course you need to look past Huntin Fool's picks to find draw odds of 50 to 1).
Wyoming: with the point system in place, you will never make it to the top of the heap to draw a preference tag. You'll need to apply where random tags are available to non-residents with draw odds from 0.5 to 2%, depending upon the area. $100 per year to pay for a point (not optional).
Utah: since you're from Utah, there's no reason to cover this.
Oregon: Both California and Rocky's are available. There is a high non-refundable license fee - $140.50. Non-residents have a set quota of tags. There is no point system in place for sheep. Draw odds, of course, are steep.
Arizona: very few tags, no non-resident quota, & high application costs. The state has very good rams, though.
The cost to play the state lotteries every year is huge, with non-refundable fees that could total close to $1k.
If you truly want to hunt a North American sheep, your best bet is to find a cancellation Dall hunt with a quality outfitter and go. However, you could also get very lucky and draw your for year for a bighorn.
Another resource to check is wildsheep.org's community forum. Ramdreamer posts all the states information with all the details regarding the draws.