I used to move Gold Crowns with a Dodge Grand Caravan. Not ideal, and certainly not meant for the weight, but it worked.
I would lay a moving blanket down first, and then lay the first slate on top of it. So long as you pull all staples from the bottom side of each slate liner, you shouldn't need to worry about covering each slate.. Just lay one on top of the next. However, if using a Grand caravan (or similar), you will want to have a small scrap of 2x4, to support the front edge of the slates.
Once the slates are loaded, I would cover them with another moving blanket, then load the long frame members. The should slide up between the front seats. GC 1's & 2's have longer frame members, so it will be a bit tighter fit, but still works. On top of the frame members, you can place the long side skirts, straight up between the front seats.
From there, you should be able to jigsaw everything else into place. I prefer to stack the skirts face-to-face, and stretchwrap everything together. I also wrap the rails together, 2x2, then all 6, and wrap them completely with a moving blanket. I also wrap the frame members together, and I generally bring a small storage tote for the castings and miscellaneous hardware. Usually, (2) 1 gallon freezer bags, and maybe a couple of sandwich bags should do it. Also of note, a complete set of balls fits perfectly in a 1 gallon freezer bag.
Good luck.