I live in Hamilton, 35 miles north of Sula, and hunt county on nearly all four sides of the general area you're describing. There are definitely elk in there, our herds are 20% over the F&G objectives right now, even with all the wolves. That said, expect a tough hunt physically. The better shape you are in, the better odds you'll have to score. General success odds in that area run under 10% for a hunter holding a bull tag. I hope that doesn't sound too bleak, but elk hunting is a lot tougher than whitetail hunting.

Bulls should be bugling a little still, but the main rut will be long over. The best thing about that first week is that even if they're not actively bugling, most of the herd bulls will still be hanging with cow herds. Find a cow herd and there is probably a bull in tow. (In fact, I think it's the first week of rifle season that prompts the bulls to split off from the cows. They get run around a couple times and the bulls head off for the real rough stuff to hide.)

Have fun!