If I had to get a screw to grab into that black wavy rotted plywood I would dig out as much existng wood as possible where the screw needed to grab.
I'd then mix up some 2:1 surfboard epoxy I have on hand, which is thin enough to easily saturate fiberglass. I'd use a bristle brush with about half the bristle span taped to act somewhat as a resin cup, and get the properly mixed epoxy upinto the wood, twice. Then I would thicken the remaining epoxy with wood flour, or some other thicotropic agent nd use a putty knife to stuff it upinto the recess. If gravity was priving an enemy, use a Ziplock freezer bag and a flat edge and stick of the proper height to holt flat edge to plastic.
Once the thickened epoxy cures, I would drill it then slowly and carefully tap it for a machine screw. Stainless Coarse thread.
Wood flour can be made by collecting sanding dust. I use it from a belt sander. A lot more flour is required than one would think to thicken the epoxy to a peanut butter like consistency.
Epoxy left in a cup will exotherm and cure a lot faster. Spread it out for more working time.
There are other epoxies like system 3 rot fix which can be used then drilled and tapped. I would use what I already have but perhaps buying an epoxy designed for the task would be better for the OP.
Dry rotted wood can suck epoxy out of the thickened epoxy and lead to a poor bond, whch is why I would recommend painting epoxy upinto the cavity so it can wick up into the wood, then stuff the cavity with thickened epoxy while the painted epoxy is still uncured.
I would not use any of the store bought 2 part epoxies. Epoxy needs not only a very precise ratio of resin and hardener, or parts a and B if more familiar, but these parts also need to be mixed thoroughly for a proper cure to occur.
Improperly ratio mixed epoxy, or epoxy not mixed thoroughly, might harden, but it will NOT have the true strength properties as it would if it were both mixed in the proper ratio and mixed thoroughly, and the store bought epoxies allow for a lot of error on the thorough mixing part, and some of them can also leave a lot desires in the proper A to B ratios too.
5 minute epoxies are NOT waterproof either. I have some System 3 5 minute epoxy, and I have mixed it thoroughtly using a digital scale to the 0.01 gram, and the results in my application, had me sand it off and use the 30 minute potlife epoxy.
For a good Epoxy I would recommend System 3 General purpose epoxy with their medium hardener. It is fairly syrupy though. If maximum penetration of the wood was the desire, i would use the System 3 Clear coat resin which is very thin. Their CC resin is also very slow, and one can still thicken it with wood flour or fumed silica or one of the many other thickening agents available.
If one doubts my credentials with either woodworking or working with epoxy, this is my latest completed project.
It is strong and surfs very well and getting it both strong enough and accurate enough for both these requirements required huge amounts of labor and precision, and forethought as to design and method
