I find I rarely need any supplies. I bet it's been about nine years since I've used more than gloves and a CPR mask. That was only b/c a car wrecked into a pole right across the street from our driveway, and there were five patients. Two were hemorrhaging quite badly from head wounds.
Unless you're providing a service, that you're getting paid for..and you will need all that stuff... (like Craft Service-First Aid/Set Medical/etc as your resume indicates)
I'd go with a small box, maybe a Flambeau 1872 or 2072. No worries of fluids or bio stuff soiling plastic, at least not if you clean it off. They're a good size to hold a nice amount of first aid, CPR and vitals obtaining equipment. I'd sooner go with a box, than any type of fabric, even that antimicrobial fabric will wear and tear. Nix the splints, go with a couple unitized boxes of wire splints, or a flat packed SAM. Put the sun screen in your glove box, you won't need that for 99.999% of emergencies. Nix the cold packs, they can wait till the ambulance arrives, if they can't, start removing clothing. Bandaids... Keep like five, throw the rest in with the sun block.