A few solutions, and repeating some of the above. Assuming that the rail you are talking about is top of the gunnel and the outer-side is protruding the
hull, to act like a a rubbing strake. I doubt if replacing the whole timber rail with a a plastic one will be a solid enough base to screw in the staunchions.
- replace whole of rail with timber, for other woods see above
- level top of rail with planer/sander and
epoxy glue another layer of timber on top, using timber with similar contraction/expansion properties. This 'layer' to be 10 to 20 mm thick
- as above but then in other material than wood, like starboard. Maybe not as aesthetically pleasing, but less maintenance; although most of the plastics cannot be glued with
epoxy, either use screws or a suitable gooh from a reputable supplier ie Bostik, Sikaflex, Simson, 3M etc.
- the following can be done with any of the above solutions: plane/sand the outside of the rail, and screw strips of PE (polyethylene). This makes a superior
rubrail: no splintering, no maintenance, and
parts can be replaced easily if they become looking less than new. Yes, PE is softer than hardwood, but it slides beautifully. It protects the wood that is far harder to replace. When using PE the minimum thickness I guess would be 12-15 mm. Width depends on the wooden rail that is supporting the PE. Black PE stands up better tot he sun than the white colour. Black lasts at least 20 years without any deterioration (I have this on my jetty instead of the boat). White lasts ~ 20 years, I put this kind of rubbing rails on a few boats.
- Install a strip of metal on the gunnel/rail to protect the wood/boat: ie
bronze, monel, SS.