What do you think about also having a SAM splint in the kit?
The quick clot is a great idea. Can you get those from your regular pharmacy?
Cabrito, hope the rest of your ride home was nice.
I'd recommend sam splints, though they are a little bulky. The folded ones are much easier to pack than the rolled ones.
Quick clot is sold at regular pharmacies, though I am not too familiar with it. I'd probably just use direct pressure for a good bleed.
As far as the occlusive dressing (Xeroform) that's not big enough for any real trauma. Also a piece of duct tape works well enough for a sucking chest wound.
Steristrips are awesome as is the abd. I'd recommend a roll or two of roller gauze and a fatty stack of non-sterile 4x4s. The wounds aren't sterile, the dressings don't NEED to be. Also maybe consider a few pairs of gloves. Maybe some benadryl in case of an allergic reaction.
And most importantly, an emergency blanket. Basic shock treatment is critical for a trauma patient. If possible, put their feet up to get blood to the core, and keep them warm. Even if it's 80 degrees out, their body will not be able to maintain its temperature very well.