This is my first year growing watermelon, but I've grown pumpkins before. I have always had problems with slugs--big ones and small ones. I found that there was a pumpkin in the shade that was oddly shaped and decreasing in health. I guess the slugs could tell, because they ate the entire thing until you couldn't even recognize that there was a pumpkin there in the past.
Well, the slug didn't really attack the one in the sun. I had a few small black ones underneath it (I used black cloth--or maybe it was straw, or a combination), but in the end it was OK and the slugs didn't eat it. I think they can detect when something is going to die anyway, as they tend to also eat the weaker plants--or maybe they just think it will be less work. Not sure, but they didn't destroy the others.
Have you grown watermelons or pumpkins before?
I use sluggo now and it seems to be controlling the issue. I also use a copper wire around the basil. If you are really concerned, I would invest in some copper tape or wire and attach it to the perimeter of the board. However, they might be deterred by the roughness, as I have used diatomaceous earth and it cuts their bodies.
Also, do you have any pictures?
Hope this helps!