If the ply is soft, and you just want a quick (almost instant) fix - the following worked well for me for a couple of seasons:
Lift the bench cover and cut an X in the fabric around the screw hole. Use a large wood bit to cut out a hole just a mm or so smaller than a brush shaft (which you have spare
) Cut small plugs of shaft, taper them slightly with a grinder or file and tap them into the ply base. If the base is or gets damp the shaft plugs will swell and lock into place. Job done.