Look up Kearl Ranch Outfitters. I hunted with them early rifle years ago and had a great time. Greg Wamsley or Clint Kearl. They own and run a lot of private ground up there that holds a lot of elk. There is a lot of other private ground in the unit as well. Not saying there's no public because there is but if your a non res and wanting to put the odds in your favor give them a call. I live 1 1/2 from the unit and have spent a ton of time on the east side of the unit. There is elk but it can be tough. Congrats on the tag! Either way you'll enjoy the hunt, its beautiful up there!
Side note: I went the guided route because of a situation at the time. Drew the tag, dad had the big C and want to experience a elk hunt. They accommodated us perfect. In the end had a great trip, chase elk everyday, great bull tagged, and dad is good to go!