I'm no expert, heck compared to what some guys take, my bucks are dinks. But, I'm passionate about backpack hunting high country muleys in Wyoming's regions H and more specifically G. When I was 18 I packed a backpack full of clothes and moved from Salt Lake to Jackson and then a few years later to Alpine, fast forward 12 years and I'm dug in deep like a tick where the sun don't shine and I'm not leaving until I physically can't make it into the high country anymore and at that point in my life (hopefully) I'm cashing in all my chips and moving to the coast to start a new life of fishing and gathering whatever kind of delicious critters I can find in the sea. Until then I spend about every weekend all spring, summer, and fall up the Greys and more specifically, come September I spend my time between 9,000 and 11,000'. Yes there's bucks from the bottom to the top but me personally, I prefer the solitude, the altitude, and having to work for mine.
If I was in your shoes here's what I'd do if I was going at it DIY.
-I'd start with maps, Google earth, or both. Pick a high 10-11k' peak or ridge that's only accessible from one side...Greys, Salt, Pinedale side, wherever, and try and stay away from pack trails. Make sure it has secondary ridges that drop off into timber or cliff country. After day 1 you'll find your bucks using the secondary ridges.
-figure out a water source; spring, lake, creek and plan on starting around that.
-if at all possible, scout. Even if it's just a weekend driving through, get yourself familiar with the topography.
-if scouting is absolutely not an option make sure you show up a few days early to get up high and have a few bucks picked out for opening morning.
-If you don't see what your looking for after a day or two of honest effort/glassing then move a few ridges. (At first you'll find the bucks in the wide open above timberline but after opening day your best bucks and most of the bucks will drop down into mixed timber/cliff/Avalanche shoot type canyons and bowls and will spend less time in the open every day.)
-I'd use the camp trailer as a home base for restocking or meat storage but I would do everything possible to not stay there (unless you feel like spending extra hours every day hiking in/out IN THE DARK)...any time spent there is time wasted!
-head up to your pre selected drainage and set up camp. Like stated before, be quiet, be scent free, be bear aware.
-glass all day long! I'm talking from morning dark 'till dark 30 at night. I find as many bucks bedded in timber in mid day as I do at sun up. When you get tired of glassing move a few hundred yards and start over.
-you will see guys the first few days especially but you should also see plenty of bucks. Pressure tapers off every day.
A few final thoughts...
Things will get tougher with every day that passes, at least for the first half of the season. With the second half of the season the weather can be a lot worse (colder, snow) but also the crowds will clear out and the bucks will start to come out of hiding to feed in the open again.
Treat it like a sheep hunt, seriously! If you find the bighorns or the mountain goats you're looking in the right areas.
Watch out for lightning up there! I've had to literally run thousands of feet down the mountain and head home in the middle of the night because you could feel/hear the electricity just buzzing in the air with dozens of cloud to ground strikes all around. After returning to camp the next day you could see that most of the surrounding ridges had small lightning fires burning on them. It's scary stuff!!
Have fun, be safe, and kill a big one!