MSU, It sounds like you've found most of the info, of the very little, out there. They sound like pretty smart birds who make you work for it! Everything I've read also says to look above 10,000ft and that you're better off spotting and stalking them rather than just hoping to pop up on them. With that said, I'm not sure what benefit a dog would offer other than the optimistic hopes of a retrieval. I personally don't own a dog but my good hunting buddy will be leaving his at home rather than dealing with the constant stress and worry that the dog will end up running of a cliff, which judging by their preferred terrain, is a very real risk.
Lamoille canyon and it's nearby peaks and cliffs sound like the hotspot for activity, although I'm sure they're spread through the range with only the difficulty of terrain keeping the other spots from being as "pressured".
I just picked up my permit today, and it sounds like someone else was down there today doing the same! Perhaps somebody off of this forum? I hope we all get some days out there and can come back and report on what we learned/saw/didn't see. In all honesty I'm going into this first effort hoping to simply lay my eyes on one. As with any animal, there are many things to be learned before you're given the gratifying opportunity to pop a shot off at one. So anything beyond just seeing a rare and elusive animal will be a bonus in my eyes! And further more, it gives me a reason to explore some new country!