We decided to take it to the car wash and spray it down - normally you have to be very careful when getting water on old wood because it could warp. But I decided it was worth the risk since it looked like the back had already been exposed to moisture (rippled). Besides, I wasn't going to spend an hour cleaning all the dirt and dust out of those little cubbies.
So it did ripple the back a bit more, but I wasn't concerned. The problem that developed had to do with an unforeseen layer of paper on the backing. I had no idea and the paper was destroyed by the water. Thus the reason it took me a few weeks to get started on the project. All the paper had to be taken off and it was in pieces and stuck under each slat.
I asked my grandson, Myles to take as much off as he could and then I took my handy dandy Allway Contour Scraper to the rest, planning to leave just a little for an old-world rustic look.