I am no expert, but since I am planning to build a boat I have done a heck of a lot of reading.
I would use marine ply laminated with thickened epoxy. Tabbed to the floor with two layers of 400g biaxial. Everything covered with epoxy to insure it is protected from water etc.
Abrade the hull where the stringer is to go in then make sure that there is a good bead of thickened epoxy between stringer and the hull and the stringer sits on this evenly. That will help to reduce hardspots where there is uneven loading of the stringer onto the hull. Fillet with epoxy thickened to peanut butter consistency, and 150mm 400g fibreglass biaxial tape over that after it firms up some, but before it fully cures. Offset the layers of tape by 50mm to give a smoother transistion.
Add cleats/frames to get a good bonding surface and reinforcement then epoxy glue over that. Precoat the underside of the sole (assuming marine ply?) with two layers of neat epoxy and then lay it in.
If you need to let the epoxy fully cure between steps then you will need to wash any amine blush off with water (use soap but NO solvent) and a scrubbing pad. Dry with paper towels.
I have the plans to build a boat of similar dimensions to the SeaNymph and that's the layup method used in a nutshell.
The bateau website has many examples of a boat being built from scratch.
I have linked to the bit where they install the stringers here. This particular boat is a bit lighter than yours so I would beef things up a little but follow the same process.
If you browse that site they also have a rebuild and repair thread. Plenty of experienced advice from people who have built boats, and the site owner is a qualified marine architect.