I wouldn't waste that much free time on an elk. I'd get one of the unlimited sheep tags in MT and I'd be on the mountain at least 3 weeks before the season opens, find a good ram and watch him until opening morning. Then I'd take the ram.
MT is the only place that sells unlimited over the counter sheep tags and they are for areas that are spooky rough. The season ends when the prescribed number of rams are taken which usually happens by the 2nd or 3rd day. Mostly locals take the rams because they know exactly where to go which is why I would be camped out with the rams keeping tabs on them.