Nothing wrong with putting 3/4 inch Pro Balsa back, to keep the weight down vs. 3/4 inch ply which will be very very heavy, a bit more expensive though than marine plywood which comes in 4 x 8 sheets, and marine plywood doesn't appear to fit in one cut on your cover.
So butt them with thickened resin in the gap, so there is no gap.
If going marine ply, no reason to cut into checker board unless you want to play checkers!
Balsa comes in 2 ft x 4 ft sheets, butt it all together tight with thickened resin. Can buy on internet the stuff rolls up since it's bonded on one side with a glass mesh.
The wet problem has nothing to do with choice of core material, it wasn't sealed properly, probably at the screw holes or deck plates.
So make sure you do it right, over bore and core all holes with thickened resin from bottom side - redrill holes from top side after they cure.
I'd lay that cover on a very flat surface, I use my garage floor, 3/4 oz mat or 1.5 oz mat between wood (prewet all wood) and cover, weight it down with two bags high of 50 lb home depot sand clear bags layed flat. Use shipping package clear tape to cover topside surface otherwise resin may seep over side and get onto gelcoat. Make sure floor surface is smooth to the hand, no pebbles or anything. 3 or 4 mil sheet plastic down.
Keep sanmd bags away from edge of wood so you can fill the gap wit thickened resin as needed. Same goes for deck plate area gaps.
After cured, wet out and lay up the facing side.
Use two layers of 1708 or 1808, whatever you get.
What did Grady use on balsa?
If you make yours at least as thick, or better yet thicker - will feel more solid to the foot. 2 layers of 1708 will beat Grady's 1.5 oz mat, if that's what they used.
I would stay with lighter Pro Balsa. I prefer epoxy resins myself, nothing against the others. Just less shelf space needed.
Raka's 127 is perfect and easy to work with, no odor, lighter viscosity, plenty of set up time with slow hardener, economically priced, ships out same day, ask Larry for any advise.
I have no affiliation with Raka.
Get my 1708 there on the roll, silica, foam rollers, everything.
Good luck.