are you only keeping spares on the truck to use as back-ups at shows?
my show supply is a much smaller amount than what i normally keep at the school. I tend to bring more of the heads that are likely to break. I usually take 2 snare top heads, 4 bottoms, 2 full sets of tenor heads with 2 additional 6,10,and 12" heads. These heads are kept, unboxed, in one of those big, "deluxe" cymbal bags with the front pocket. I also keep some spare harness parts, tension rods, keys, etc in it in case of emergency. It travels with us until we're about to head to the gate. I usually drop it at the truck on the way.
I also bring an extra 18" and 20" bass drum head because they are the most likely to break during warmup. it's been a while since i've needed one, but it never hurts to have them just in case. these are stored in their boxes flat against the wall of the truck.
When they are stored at the school they are all stacked vertically in the boxes