One thing that I have in my kit that isn't on your list is a tire plug kit. If you're carrying an air compressor it makes a lot of sense to add it. I've been able to remove a nail and plug the hole, then re-inflate and be on my way without getting the jack out and the tire off.
I'm a big fan of tire plug kits and have used them in the past. The focus of this post was more getting you back on the road quickly. The only thing about a plug is you should still take the tire to a shop and let them patch it from the inside. (Though I drove on a plugged tire for a couple of years and it was fine, at least for a farm truck.)
One thing that I have in my kit that isn't on your list is a tire plug kit. If you're carrying an air compressor it makes a lot of sense to add it. I've been able to remove a nail and plug the hole, then re-inflate and be on my way without getting the jack out and the tire off.
I'm a big fan of tire plug kits and have used them in the past. The focus of this post was more getting you back on the road quickly. The only thing about a plug is you should still take the tire to a shop and let them patch it from the inside. (Though I drove on a plugged tire for a couple of years and it was fine, at least for a farm truck.)