I'd just rebuild with the proper cutout using a good quality arborite/formica. Corian style counters are in vogue nowadays, but they make creating a decent fiddle that works and looks right more difficult. You really need some kind of edge on the countertop to prevent stuff from sliding off in wave or wake induced motion.
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"