FWIW wood and stuff under bedliner doesnít survive well in boats. Not a waterproofer. But everybody does it because itís easy.
However, a layer of fiberglass mat and polyester resin, top coated with rattle can oil based paint (fiberglass resin unpainted can absorb water) DOES do quite well in boats. Something to consider.
I second that. I've used the fiber glass and resin combo on MDF many times back at an old job I had. Works very well. However, if you don't need more rigidity, or expect the console to be hit very hard, coating the MDF in the resin only will work great. I just did this on a project recently. Water puddles on top of the resin as expected. The pictures you sent aren't showing up for me, but if you have any exposed end "grain", just make sure you coat those well. Possibly even sand smooth and do a second coat. Another thing is to make sure you round off any sharp corners so that if/when something hits the corner, there's more surface area to help prevent the resin from cracking if hit hard enough.
Edit: Finally got your pictures loaded. I would definitely used fiberglass matting. The woven type, not the chopped.