Are you using beadboard as a backsplash?

I've seen a beadboard backsplash protected with a sheet of perspex where it ran behind the sink. It worked. But that's about all you could say for it. Save your beadboard for the sides of your island or some other place where water won't be an issue.

One of my favorite architects, Gil Schafer, uses beadboard a lot in his kitchens. He places a small piece of the countertop material at the bottom to avoid the problem that you refer to. His kitchens have a beautiful period look to them as a result. Here is a link to his website--browse the photos of the kitchens and you'll see what I mean:

https://gpschafer.com/portfolio/rooms-and-details/kitchens-pantries