How to secure screws in plywood going with grain??

Fasteners in tension are much weaker than fasteners in shear. I would get a steel T section and drive the center section into the rotted wood then drill from the FG outer skin into the T and install screws. This will provide a bearing surface and carry the bulk of the load. Use your existing holes in the section that fell down to transfer drill though the T section and then screw in place. Good luck on your project, and let us know how you make out.