First I would like to say that your idea of a trauma car-FAK is a very good idea. A car-crash is a good place for many people to get very hurt.. I've got one myself.
Your list also seems good. Some things you should add:
- Gauze, lots of the stuff. Make sure you have 4x4 and kerlix-rolls. The more, the better
- more gloves and a pair of working gloves
- flashlight and safety-vest
- lots and lots of tape. a Roll of Duct-tape is also usefull
- blankets, both wool and mylar
Also, realise that quick-clot and CAT are last-resort means to stop a bleed. Use them only when all other methodes fail.
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''It's time for Plan B...'' ''We have a Plan B?'' ''No, but it's time for one.'' -Stargate SG-1