Your desire to get a grand slam while beginning to apply for sheep tags now at the age of 34 depends mostly on extreme luck or money. At 37 years of age, I finished my slam in 2005 on a budget but also had the advantage of being in on the ground floor of some of the state preference point systems. I worked as a guide to get my first dall ram, drew a WY tag and went self guided, scored a last minute deal on a stone ram in BC, then drew a UT desert tag and went self guided there as well. If you're like me and can't afford to pay $125K to collect your slam, there are a few ways to go depending on just how obsessed you are.
1. In Montana, you can buy an unlimited bighorn sheep license "over the counter." You apply through the draw but are guaranteed a tag. The country is tough (what sheep country isn't), harvest quotas are tight, and there aren't a tremendous number of rams, but this is the only way you can actually hunt Bighorns every year in the lower 48 without facing ridiculous drawing odds. Given your age and probable physical condition, you should be able to do your research, figure out the country, and kill a ram within 3-5 years' time. There is no greater "do it yourself" hunting challenge in the lower 48.
2. Cancellation hunts are a way to go on a trip at sometimes half the normal cost. For instance, I went on a Dall Sheep hunt last year in Alaska for $5,500 because a client had injured himself just before the hunt and couldn't go. I put everything together on a week's notice, had a great trip and shot a nice 37" ram. If you have flexibility in your work schedule, and don't have unlimited funds, this is a way to go. Just let outfitters know at shows or through other inquiries that you are interested in getting on a cancellation list. Several of the booking agents publish cancellation hunts as well and you can keep dialed in to them.
3. Move to a place where you can hunt sheep as a resident. Alaska (Dall), Yukon (Dall or Stone), or British Columbia (Dall, Stone, Bighorn) are three places that come to mind. Again, this depends on how free you are to do something like this and how obsessed you are with sheep hunting. I know a few people who have gained landed immigrant status in Canada because hunting was that important to them.
4. Apply in every state that offers sheep tags and buy every raffle opportunity you can find. This requires you to front a lot of cash ($5000-$7000) and could cost you about $1500-$2000 each year even after the state application refunds but the odds are that you'll hit at least once in the next fifteen years. If you're not dead set on killing a desert ram, you may just want to save that money and spend it on a couple of cancellation hunts for dall, stone, or bighorn.
Good luck with your quest!