I have tried sticking the balsa sheet to the polystyrene, and while it does work, getting it to stat in position while the glue goes off is a real pain, firstly it takes forever for PVA to set on polystyrene, and second, as soon as you coat the balsa with glue, it wants to curl, the solution was not very scientific, I stuck it in place with sticky tape.
Another new technique I tried was a hot glue gun, I gather this would not produce a water proof connection, but for sticking large parts onto vertical surfaces which will later be glassed it is idea, again there where some lessons learned, once you start, the glue just keeps on flowing, using almost the complete stick each time, so not a system to use unless you have to, also, keep it away from polystyrene, it just melts the stuff and you end up having to make repairs.
So here is the picture so far, quite a lot of the starbourd side and stern have been strenghend with plywood panels.

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