Congrats on drawing that tag. I have a couple of buddies that have hunted it successfully and both have had pretty exceptional experiences. Can't say I am not a bit jealous. I have been applying for 15+ years and haven't touched a sheep tag yet...
After your get your mountain hunting kit pretty close to dialed, I figure that lightening your load by upgrading gear usually costs about $1k per pound. When trying to justify spending the money to shave ounces, I can't help but think that giving up beer for a month or two would cut more weight than a couple thousand bucks every would, but what fun would that be...
For the last handful of years, I've been doing a solo hunt for the opening week of sheep season and have been able to get my solo kit down to 50lbs all in. Still heavier than I would like, but manageable for high mileage approaches with significant elevation gain. More more than that on my back really increases the fatigue factor for me. I don't know why but the difference between 50 and even 55lb seems very significant to me.
When getting packed up for these trips, the load is always feeling and looking great until I add food. Damn I hate packing heavy ass food and water around.
Here are some quick thoughts looking at your list based on what I would consider taking on this hunt. As others have said, you list is pretty darn solid and you've got a lot of high quality, lighweight stuff in your kit as is.
-One knife is fine. Tuck it away someplace safe and be really careful not to lose it. The thought of getting an animal down 20+ miles from the trailhead without a knife to break it down has kept my awake at night more than once...
-Ditch the paracord, or if you must have it, take a shorter length or something lighter weight like braided fishing line, seine net repair twine, etc.
-Ditch the pillow, puffy layers in your sleeping bag compression sack works fine.
-Ditch the water filter. Above treeline in your zone any running water will be fine to drink. Keep an aqua tab or two in case you wind up in a water crisis at lower elevation, which would be highly unlikely.
-Gaiters. If for some reason you wind up with knee deep snow on your hunt they would be worth having, otherwise you can get by without them.
-Ditch the inreach mini. Your phone has sat texting which would cover your needs for comms, weather updates, etc. right?
-Smaller battery bank like the Goal Zero Flip 24 or 36 should be adequate unless you plan to spend a lot of time looking at your phone. I usuall use mine for a few photos, OnX checks, etc. otherwise keep it tucked away and/or turned off.
-Wipes. Several companies make dehydrated wipes that you add water too. Saves a little bit of water weight in the pack.
-Spotter and Tripod. I don't think I would be taking a spotter on this hunt if I was going to be happy with any ram and not try to pick out a big/old one. Based on terrain and likely proximity to sheep, your binos and context should be fine for finding rams. Ditching the spotter and tripod cuts out darn near 4lbs. If you want the spotter, consider a lighter tripod like an Aoka
https://www.amazon.com/AOKA-Compact-Lightweight-Capacity-Travelling/dp/B07PK9Q627 that only weighs a pound. Swaro ATC or the Vortex Razor 13-39 would cut a pound off of your spotter weight.
-No need for a bino tripod adapter.
-Pistol. Could probably get by without one without losing too much sleep at that time of year. That having been said, I'd probably be taking mine on this hunt. Maybe try to borrow a smaller, lighter pistol and only carry 5-6 rounds. The GFI bino link holster will save you some weight and bulk and it works much better with your bino harness rather than layering two rigs on top of each other.
-Sleeping system. Upgrading to the lightest-in-class bag, pad, and tent appropriate for anticipated conditions could cut your weight here down to about 4lbs, but those are all pretty high dollar items.
-Puffy. The SG Grumman down jacket would save you 4-5oz.
-Possibles Pouch. Delete maps, firestarter. Put a few wraps of gorilla tape on your trekking poles.
Ditto on the spare socks!