Divinycel, Coosa... nice products but expensive. Weight savings is negligible, given the square footage of the hatch compared to weight of the boat.
3/8" might be fine... but go with 1/2" - you're only talking a couple bucks here - not the place to cheap out. And, again, weight is inconsequential.
When I rebuilt my entire floor (and hatches), I used marine plywood (all layers have waterproof glue and there are NO voids anywhere in it, unlike regular or even exterior plywood) for the floor (first, FULLY encapsulated with resin). But knowing it would be really easy to redo the hatch, I decided to try something different. I used that purple-ish foamboard insulation from Home Depot. I experimented with it first, but it's now been about 5 or 6 years and it's still rock solid.
FYI, there's a number of threads on here about this process (including my write-ups about the foamboard) - with lot's of information in them. Just use the search and you'll find them. BUT... lightweight mat between the core and the hatch, then a single layer of 1708 over the new core.