^^^^
Using a towel or 4 is the simple solution. If you wipe the board the only bit that stays a bit wet is the footstraps. Put the board in a bag and that water won't move.
Wiping the sail dry leaves only a bit of damp in the mast sleeve, and not even that on a warm day if you have a few minutes to spare and let the sail dry before you unrig.
Putting shelves in the van so the gear isn't resting on the carpet and air can circulate to keep it dry would be better than making a carpet sandwich between plywood and the van's floor.

I have fully waterproofed the floor by using a rubber floor mat and sealed all the edges so basically a mini bathtub. Water from the footstraps sips in there and I store the "wet" sail and boom there until I get home. It really ain't much water, but surely will ruin your van/car if you sail regularly in salt water.

This works pretty well for me. Photo is from when I was still building the van but you get the idea.

I use a kind of a hybrid system, 3 boards horizontally on the rack, and one to the side IF I need it.

But as a side piece of "rack news": to keep everything tidy I just made a little modification to two sail bags to be able to suspend them from the ceiling of the van. Just two brass grommets each ($8 at Amazon www.amazon.com/dp/B000BPNOMU?psc=1), 4 short shock cords out of 5/16 and this cool hooks www.amazon.com/dp/B08M62P352?psc=1, and bingo two sails are neatly suspended from the ceiling.

Main reason for suspending is that I like to keep the visibility through the rear window. The set up, just between rack and suspended sails, can fit more than I need. That is 3 boards (+1 one to the side), two booms (three with one on top of the rack that has an extra level in front), 4 masts and three sails at the bottom of the rack, two sail suspended. No rear window occlusion, and space to the side for my MTB or my "nap mat". I think I am ready to conquer some far away island with such a fleet