I this on the other thread as well. There are at least 6 outfitters that operate in the Absaroka-Bearthooth wilderness area, that I know of. Together they probably run 100 guys through a year between them. According to the MT FWP harvest stats, 14 elk were harvested in 2012 in that area. That included cows and calves.
Its gorgeous country but not the most productive area in the state to harvest an elk. Access to that unit is very limited and unless you are using horses or are planning on bringing five guys or more and going home after the first elk is harvested you are probably not going to have an enjoyable hunt. The wardens in that neck of the woods take meat spoilage very seriously... However if you do decide on a hunt in that area the closer you stay to the park the more likely you are to catch a bull possibly coming out to look for cows coming into estrous that time of year.
Best of luck to you in your planning and hunt. Not to discourage you in any way from hunting in MT but Colorado has many great options as well for the budget conscious DIY hunter. They also have a muzzeloader season for elk that would fit your timeframe.