If it was mine… I’d use the same materials used to make the lid. My suspicion is that the lid is strong enough, but, flexes to much. To make a fiberglass laminate stiffer, you have to make it thicker or deeper, how every you want to think about it.
So, to make it stiffer, add some thickness to the laminate. (This will have the side effect of also making it stronger.) Cheapest effective coring is regular old 1/4" plywood. Encased in resin, it’ll last forever.
Leaving room around the edge of the lid for hatch gutters and hardware, to the following.
On underside of lid…
Cut a 1/4" piece of plywood to fit the underside of the panel leaving about 1" border all the way around. If your hatch is guttered, you’ll need to stay inside the gutter, then 1" of all glass border, then, plywood. Cut the plywood panel with a 45 degree angle, then round the top of that 45 deg over to allow glass to wrap over it easily.
About 4 hours prior to laying up on the lid, coat the plywood with resin of choice. Allow to tack up and keep it clean. Do the following prior or just make sure your sanding dust does not get on the new work.
Sand the underside of the lid with 80 grit sand paper, some. You want to remove ALL of the original surface which might have waxes or other contaminants on it. Hopefully, the glass fiber is not to deep in. If you can get to it with a little sanding, get just barely into the glass leaving the face slightly fuzzy - nearly microscopic. IF there is a LOT of resin to go through before you get to glass, don’t worry about it. If you can get to the glass and leave it very slightly fuzzy, that’ll improve your bond.
Vacuum it clean.
With a clean (no fabric softeners or fragrances) white (no dyes, print, or applied decals) rag and just enough acetone to damped the rag, wipe the surface clean. Do NOT use a lot of acetone. Part of why we just coarse sanded that surface was to give it some ‘tooth’. A lot of acetone will melt that surface a little and s
new lid is thinner and weaker than the original.