Hey bud:
There is an unlimited sheep hunt in Montana. It is very tough. One of the reasons it is unlimited is because it take an act of God to get a ram in there. I went three times in the unlimited. Killed a ram once got skunked once and turned down a legal rams once. The year I got my ream there were 149 tags issued for the area I was in and two of us killed rams. the season never did close. I kept track for a while and there was a year where they killed like 18 rams the first day. So the year can make all the difference. However even with a good year your chances of success are extremely low. Also in a good year for the hunting the season will be three days. It's closed on a 48 hour notice when the quota is met. Most of the time the quotas were like four rams.
If I was to look for your best chance to hunt a wild sheep on the cheap... it would have to be an audad ram in NM or a free range one in Texas. There are some there and the prices are relatively reasonable. While it may not measure up to the challenge of the four native wild sheep of north America, they are still a true hunt and very rewarding.