Big Horn Mtns (Solitude Trail)

I can't open your gearlist atm (issues on my end, not yours) but I'll address some of your concerns.

I almost always carry 4L of water carrying capacity. Granted I live in a desert and am somewhat paranoid about dehydration. Then again water reports are unreliable, especially with the nationwide droughts we've had the past few years. July/August is about the peak of summer when water is at it's scarcest. I'd bring 4L and just fill up as conditions warrant (if perennial streams are little more than mud puddles than top off). Wyoming can be surprisingly dry in areas but I don't know about the Big Horns or how many lakes you'll come across. A light 2L platy or similar rollup bottle is very minimal weight and space but provides a large safety margin on a week long trip.

As for filter, since it's alpine region you can probably discard it if you're using stream water. If there's any cattle grazing though just remember that aquamira takes 4hrs (or more if icy water) to work with cysts so a filter is more time efficient.

Bring a puffy. Summer blizzards are not unheard of in any alpine environment in the US. You're fairly far north and at elevation, doesn't take much to give you a few inches of snow. A thin down puffy is probably the lightest way to give you some warmth margins but you also have to factor in that if you do get a cold snap you'll probably have freezing rain and sleet so a synthetic might be more useful.

I like to mix and match, if a synth sleeping bag I'll carry down clothes or vice versa when I'm unsure of weather conditions. That way I'm maximizing weight savings while mitigating risk of wet and sloppy weather.

Longer hikes in unfamiliar terrain I tend to be much more conservative than a local overnighter. Too much "new" and time for me to push the gear envelope too far. I still carry a minimum of gear, I just go for slightly more robust or versatile gear than I'm willing on a simple overnight sufferfest trip.

I too plan on hiking the Solitude Trail this summer (probably in June if the snow pack allows) along with the Absaroka/Beartooth Wilderness and the Wind Rivers. My pack list is very similar to yours with a couple of differences.
I will be packing a down puffy for warmth in evening and for the inevitable snows/sleet/cold rains. Wool liner gloves suit me better than leather which tends to get slimy and non insulating when wet. Wool doesn't catch fire like fleece will also, so is safer around stoves or wood fires (seems like there were open fire restrictions last year in the Big Horns). If there are fire restrictions will one can of fuel be enough?
One might consider a sun hat for that elevation also. The sun can be brutal, especially above timber line. I also carry a bear canister for the occasional black or brown bear. Can you hang your food?
Around here (Black Hills, SD), which is not far from and similar to the Big Horns, I catch trout with a double hook Bass setup and worms for bait. Just out for meat, no sport involved!
Seldom are you over an hour from a good water source, either glacier run off, or alpine lake. I will only be carrying 1 liter of water with a 1 liter backup container if needed. Water is clear in the Big horns. I have not had problems with filters clogging from silt. It's a wilderness area so live stock are not a problem. Many moose though.
Might see you on the trail!

My packing list is made under the assumption that I will be able to have fires if needed. If there is a fire ban in effect I will likely bring another canister of fuel and perhaps even a light pan for cooking fish. I also choose to bring leather gloves for the same reason. I like to have a pair of gloves that will protect my hands (especially for processing firewood). If I were not having fires I would likely bring wool gloves as well.

I'm thinking the down jacket is going to be nice to have. I've been looking at the Demaree Canyon from GoLite. I've been happy with their stuff so far and it won't put me in the poor house.

I also always bring a full brim hat. I don't add it to my list because I'm always wearing it.

Bears were another question mark for me. I don't know if there are enough of them in the Big Horns to be a concern and whether or not there are enough decent locations to hang. I kind of assumed that there will be much fewer bears above the treeline and so not being able to hang would not be a major concern. I have mostly backpacked/camped in northern Minnesota and so never had issues finding a tree to hang food.