You guys have said "Utah draws stink". That's true - all draws stink, but without them we wouldn't have any big elk to brag about. Maybe we shouldn't worry about getting a "400 class" elk, and just settle for having a good time hunting a "good, mature bull". It took my brother 12 points before he drew a LE elk permit. He got a nice "350 class" bull and was very happy with that. I went with him, and the experience was almost as good as doing the shooting myself. (I'm still waiting for my chance).
I drew a moose permit with only 8 bonus points, I didn't take the biggest moose I've ever seen, but I got to go moose hunting and it didn't take 20+ years to draw. Be flexible on which hunts and which locations you're willing to apply for. Check the draw odds reports each year. It's not a fool-proof way to get permits because "draws stink", but it helps. My brother got a bison permit with 8 bonus points. I hunt with 2 brothers, and having one of them draw a tag is nearly as good as drawing my own. Maybe we're just lucky?
Share the hunt, enjoy the experience! Stay away from hunts with poor drawing odds. Other hunts with better odds have excellent quality game, they just don't get the same amount of press. The bottom line is to keep trying, whether its Utah or some other state.
I've been trying for a turkey permit for 8+ years, and finally drew one. Except for the travel, I can get non-resident OTC turkey tags in Washington state for about the same cost as my Utah resident turkey. Shop around for better deals in neighboring states.
A few websites like Away Hunting and Bighorn Outdoors have "Swap Hunt" forums. Maybe that works too. The two biggest problems I have are time and money. The third problem is finding acceptable partners for new hunting experiences. My brothers are great hunting partners for Utah deer and elk, but they're not interested in a lot of other things that I may want to do.
It was also said that hunting is a rich man's game. Also true - and its one reason to hunt predators, upland game and waterfowl. Find ways to make the money you have do the most it can.