Soft Hatch Lid

[Lady of the Lake]

One of my fiberglass deck hatch lids is soft and in need of repair. Looks like there is a piece of marine plywood glassed into the underside of the lid. Looks like that wood has gotten wet and rotted, resulting in a soft lid with no supporting structure on the underside. Any recommendations on the best way to repair this? Should I just cut the old plywood out and replace it with a new piece and glass it back in? Or is there a better way? How about StarBoard? Won't rot but I have heard that adhesives don't work well on it. Any ideas? Anyone had to do this?

Thanks,
Sam