Consider, if the material you have is like Formica (a thin flexible sheet, like 1/16" actually made of layers of paper embedded in resin) and not Corian (a thick and totally inflexible synthetic stone) then you may be able to just repair the damage--without any screws.
Formica and similar materials are just glued down with a contact adhesive. Traditionally the mustard yellow kind although there are good water-based white ones available now as well. If you can clean out that delaminated area and then apply a contact adhesive to both surfaces, once you set it back down (and clamp or weight it) it should set up perfectly, good as new.
Epoxy or urethane adhesives would also do, but contact cement is way cheaper and designed for this job.
"Tile ?????? There is no way to 'seal' the grout, " Yeah, actually there is. Tiled kitchens have to pass health department and USDA standards all the time. You start by using an "epoxy grout" which is epoxy-fortified similar to the way that resin impregnates fiberglass. And an "unsanded wall grout" rather than a floor grout, which contains sand to provide strength when it is walked on--but won't set as tight.
Then there are surface sealers which also help. Regular countertop cleaning is all it needs after that. But for tile on a boat...Geez, Mick, this isn't gonna wind up on HGTV as a frilly boat show, is it? :-)
$2 for the contact cement, some scraping, a weight overnight, good as new.