I do have some experience with this sort of thing, but please decide for yourself what method of repair you think is best for your situation. There are several ways to successfully solve your problem, each with its own pluses and minuses. A repair similar to this has been holding fine for 7+ years now on a cockpit locker hatch on my 34 O'day. I step on the hatch every time I board the boat, and it does not give under my 220 pounds. To address your question, I probably would not lay any fiberglass matting in between. It may not hurt anything if you did, and it could even help. My concern is that if there are any tiny voids between the wood and the lid that it may interfere with the bonding of the two pieces. Your lid is only 1/2" (or less) thick, so the plywood, if securely bonded to the underside, should provide ample strength even without any fiberglass mat. Another thing I thought of; be sure there is enough clearance between the bottom of the repaired lid and your anchor winch and/or windlass. If the space is too tight you might be able to create enough clearance by cutting a hole in the board in the appropriate spot. Good luck with it!