Take a first aid class designed for addressing wilderness issues, or pick up the NOLS Wilderness Medicine guide. The regular first aid protocols are not intended for issues that are 10+ hours from professional level medical care.

My kit has bandages, gauze (a small roll, a bunch of patches of various sizes, sterile), sport wrap, immodium, various headache pills (I need prescription migraine meds, sinus meds, and then there's regular old ibuprofen, plus some naproxen), sudafed, benadryl to help with allergic reactions, a tick puller (one of the few items that's gotten several uses), two pairs non latex gloves, leukotape (for blister prevention), some blister pads/bandages, alcohol swabs for the sterilization of the microtool, and some neosporin ointment. I put a few feet of medical tape around a pill bottle.

I also consider everything else in the pack to be part of the first aid kit. If someone is hypothermic, dehydrated, or having some issue that is likely compounded by dehydration (like elevation sickness) then the water filter and clean water supply are necessary. You need clean water to irrigate wounds so the hydration bladder becomes a wound cleaner. Clothes can be put into service to put pressure on heavily bleeding wounds, or layered on the person to warm them. Sleeping bags need to be wrapped around the hypothermic person. Fire starters to make fire (ignoring regulations in a survival situation) in order to signal rescuers, or to warm up the person, or make warm drinks or dry out their soaked clothes (hypothermia happens exponentially faster after falling into cold water). Pack stays, trekking pole sections, or foam sit or sleeping pads can all be splints or braces, or with a jacket the poles can become a travois for transporting the injured.

You also use plastic garbage bags, or the ground cloth, or the tent fly, or the tarp, to complete the hypothermia wrap - bundle in dry clothes, then sleeping bag, then a vapor barrier to re-warm the moderate to severe hypothermic. Placing hot water in bottles in the hands, armpits or along the thighs to slowly warm the person puts those plastic bottles or Nalgenes in the first aid kid too.

Training is the first and most essential tool in the FAK. Everything else is already there.