How strong is fiberglass/plywood sandwich plate?

Glassed. I tested a single layer of 6oz woven, balanced weave e-glass cloth on 1/8" okoume. It was surprisingly ineffective at stiffening the plywood. That does not answer your question adequately other than to say it's going to take some trial and error, and possibly more carbon than you would expect.

Carbon fiber is much stiffer than e-glass. The stiffness will follow the rule of mixtures with the resin. Since the carbon is much stiffer than epoxy, the resin stiffness is insignificant in the crude test that I am suggesting. The thing to remember is that a hand layup will have off some off axis fibers and better than half the volume will be resin, so the stiffness will be less than half as much as the same, albeit unattainable, thickness of 100% by volume carbon fiber. That is still pretty darned stiff. I think e-glass has an elastic modulus of 10,000,000 psi (lots of GPa) G-10 fiberglass epoxy circuit board is a good solid layup of balanced weave e-glass cloth. It has a modulus around 2,000,000 psi. in the 0 and 90° directions and my guess is 500,000 at 45. I could look it up, but this is accurate enough here. There are lots of promising property numbers that get watered down in composites. Metals are so much simpler to predict. Looking at these numbers, a thin sheet of aluminum would be stiffer than G10 at the same weight or less. You might be able to beat that with carbon.

Make some narrow strips with the grain running 0°, 45° and 90° to the long axis of the samples. They should all be the same. 2x12" is a suggestion. My one picture of some 1 1/2 x 6" pieces of 3mm okoume loaded with 1/2-13 x 2" bolts is only showing about 1/2" of deflection on the 90° specimen and very little at 0°, so 12mm ply wouldn't deflect enough at 6", better to go a bit long. The panel orientation makes a lot of difference, so don't build one sideways and expect similar results.

Add layers to both sides of the the samples and bend them by clamping one end and adding enough weight to the other to get an easily measurable deflection. They are fast and easy to make, so you can dial it in without a lot of trouble. Offhand, I would suspect that you will need quite a few layers to match the stiffness of 12mm plywood with carbon coated 6mm. Fiber direction is very important because the stiffness drops off precipitously with off axis angle. Anything over 10° starts dropping fast. Carbon fiber is noteworthy for lousy impact resistance. I tends to take a single blow, but will be severely degraded by that blow. Strength after impact is a common test. If you want impact, add some kevlar.

I don't know that surfboard resin is polyester since any surfboard with a polystyrene core would be dissolved by the resin. Since I have no doubt that you can read the label, you already know. Polyester is famous for peeling off wood. if you go there, prime the wood well with lacquer. Polyester stripper canoes were made successfully back in the day by a few people who primed with lacquer. I can't tell you which lacquer brand worked best because the only one I knew of was discontinued ages ago. I suspect that almost any decent lacquer would be similar, but assumptions can bite you on the backside. You need to try some to find out. Nobody uses it anymore.

45 pounds of 12mm marine plywood is just over a full sheet. Your break even thickness for solid aluminum is about 5mm for the same thickness. 2 layers of .5- .75mm aluminum laminated to a 4mm plywood sheet might be stiffer and lighter if the panels are all flat (he said without doing half the math). You could use end grain balsa and save more weight.