When I was renovating my bathroom, I had a high gloss bath panel - laminate faced board - and had to router out a channel in the back, to allow fitting the waste trap cable mechanism. And that has given me an idea....
How about going with your "standard kitchen countertop" idea, but before you install it, use a router to 'honeycomb' the reverse. You could cut through about 2/3 of the thickness, leaving a grid of full depth - around all edges, and at regular spaces.
Dont know if I've explained that at all clearly, but if you get what I mean it will be almost as strong as original but maybe 25% lighter.
Just a thought!
