The list is good! I put together a kit like that a few years ago, with things like a pocketknife (for cutting bandages), a big chunk of a white tee-shirt (for big bleeding), gauze pads, smack-and-chill type ice pack, etc. FWIW - an Epipen requires a prescription, and I wouldn't use one on someone else (non-family member) unless I knew their exact allergy situation.
I put my 'kit' inside a plastic clamshell pistol case, so that it would be in a stout box that could get knocked around and not pop open and spill. Witness the chintzy plastic cases in which most commercial 'first aid' kits are stored. The downside is that this pistol case would be hard to open if you had a hand injury. An old cosmetics case of some sort might work, too.
You can't ever have everything you need, but going beyond the lame first aid kits most people have seems wise. I made two of these kits and keep one in each vehicle that we use for kid/family trips. Bigger stuff like sleeping bags isn't in my picture here, but should be, especially for the winter.
It's good to see some discussion on this - I should upgrade a few of the lame items in my kit and be sure the rest hasn't expired.
Colo Springs, CO