Hey Jake, it's a shame we never met up while you were around here, but congratulations. The Lee Mtn patrol may have/probabaly has a list of supplies they want you to carry so I won't go too far into that other than to say that I carry stuff geared more toward airway, breathing, and circulation (ABC!) than things like splinting. I want to be able to work quickly on stabilizing a patient while calling for other stuff (trauma pack, airway pack, drugs, etc) as needed. <-This is assuming I come across a patient or am dispatched while skiing. If I'm at a station, I take the appropriate pack/supplies - trauma/airway/etc. - that are kept there.
That said, I'm not too familiar with OEC protocols, we're EMTs or paramedics where I work so some of this stuff might be outside your protocols. But for medical supplies I carry basic airways (NPAs w/ lube, OPAs) and an O2 system-compatible CPR blob/mask, aspirin and epinephrine, glucose, vinyl gloves (several pair), an assortment of gauze pads and sponges, bio-occlusive dressings, Kerlix and gauze rolls, eye pads, triangles, medical tape, bandaids (Spider-Man and Snoopy), trauma shears, plastic bags, stethoscope, a BLS guide (also available on my phone), and on some days as appropriate heat packs (which tend to break or self-activate if crushed).
I also carry non-medical stuff geared toward rapid response/stabilization and humdrum daily work. That stuff includes reading glasses, a lighter, a pocket knife and small vise-grips (or a leatherman type tool). Webbing, 'biner, mini-rescue 8, and 160' of 6 mm rope for chairlift self-evacuation, and also a couple 'biners, slings, prusiks, cordolettes, for cliff rescues (just to get me to the person and stabilize them, then call for the cavalry). Obviously training and local procedures will determine a lot of that. And whistle, pens, sharpie marker, paper pad, forms, courtesy cocoa cards, trail maps, sunscreen, radio (maybe a spare battery), and earplugs. And zip ties!
Other things I carry as needed include beacon/probe/shovel, and a headlamp.
I wear a vest instead of a pack, just a couple people where I work carry packs. But what I want to say is develop a system for placing this stuff and memorize it. I always have my things in the same pocket/place and I can reach for, say, aspirin or airways or abdominal pads or PPE or a Snoopy bandaid without having to look for it. Grab and go to work.
I think that's most of it. Again, congrats and good luck.