"Flip Your Lid"
Our anchor well lid is balsa cored ('88 model) and I found some water intrusion around the hinge-fastening machine screws. I was able to remove the core around each screw penetration with a drill bit and other small implements and then do the classic fix of filling the little cavities thus created with thickened epoxy and then re-drill each one. Our core was breached (sounds like something from the Star Trek series...) around the part where the SS sliding latch pin was installed and that part had to be gouged out and refilled with thickened epoxy for about an inch, also.
All in all, we were were far luckier than Neal.
As to putting on a new core and then a new bottom FRP layer, I would first carefully make a support for the lid when it was upside down in my shop (OK, the bench on one side of our garage -- I really wish I had a "shop") so that the proper curve would be maintained when the old inner skin and core is removed. Then I would re-core with honeycomb or balsa. Remember that weight added to the bow is a Very Bad Thing. Then I would reskin with a couple of layers of cloth -- if concerned about jumping on it just add a band of bi-axiel cloth across the center portion. Avoid mat. Besides having little strength for its weight, it has seizing in it that will not easily dissolve in epoxy resin. If you are not equipped for vacuum bagging (and neither am I) just lay some plastic sheeting over the sandwich, a layer of soft foam over that, and a plywood piece over the foam, .... and a 20# weight on top of the ply. I have done this many times to squeeze out the air.
A smarter person would build a vacuum table setup, but.. what can I say?
Note that you do not want to inadvertantly have resin running down under the lid and hardening on the pristine "top" non skid. Wax that side first around the edges and maybe tape those gelcoated sides.
I use West System epoxies for this work, but I am sure that most other brands of epoxies would work just fine.
Do not be discouraged. Even high end yachts that cost two and three times as much per pound have their major construction quirks, as any repair yard can tell you...
Ask questions. Take enough time. Pride in a job well done is a powerful emotion, and worthy...
Best,
Loren in Portland, OR