I've not hunted either for elk. Hope someone can give you a few pointers. Since the Beartooth is a tougher draw, might be hard to find guys who have much intel on that.
I have no experience in the Snowy's. The Beartooth is open to one and all for archery season and by permit only for rifle. The Beartooth is a physically demanding hunt because much of the area is walk-in only. Horses make things more doable if you have access to them. I know plenty of bulls get pulled out of there every year. Maybe you can try rifle hunting the Snowy's and archery on the Beartooth?
There is a reason the Beartooth is open to general tags during archery. It is a much better unit later in the season. There is a lot of wide open country that the elk move into once they have herded up. I am sure there are resident elk there all year, but the odds of shooting a nice bull are better later on in the year.