well you could look at Royalex, it uses the principle youre talking about i guess.
There is around a foam kayak (cpt'n America ??) how that goes as weight and durability i dont know. But trust me i spent lots of time playing with foam cores, from the spray can foam to the building sheets to end with the structural 2 parts foam, even experimented embedding various fibers to improve the core, from fiberglass strands to different canes natural and not, testbeds were rc glider models wings (stubby wings of non-gliders work perfectly with just any foam). Well they cant match wood and where you actually had results close to wood the work involved, and cost, wasnt worth it.
The material im investigating now as a core is polystyrene, not in expanded form but in the plastic form (like the plastic forks state) its light, doest break on impact (gets sort of "chewy"). I still have no idea of the bondability with glass skins though, and i have big doubts about the ease of repair of dents and cracks.
I do this for a sort of perverse fun, but yet the results are that wood is still the most versatile, practical and economic for our kind of application.

Other material to use that is worth it in my book is Bamboo, but my source is gone so that test is not doable now, still, though, we are talking about a natural material, we cant still beat nature with what we create.

: Maybe thick, sort of stiff, rubber instead of wood as a core, with something
: other than epoxy? And is there nothing other than varnish or paint to
: provide uv protection? Polyurethanes are cheaper but sound not as user
: friendly overall. Spreadable, cheap, silicon rubber would be nice. Wood
: looks nice and all but...

Rubbers, silicone included, are heavy materials to be used in a kayak, generally elastic being rubber, at that point you could scrap the core, keep a structure, add a skin that would remeber you of something rubbery... SOF!