Make sure you use marine grade.
This is the one place you need to be sure that you use marine grade plywood of the same or larger thickness. As this is your mast support and your chain plates use this it needs to be very strong. Marine grade only means that it is devoid of gaps and air pockets between the layers of wood. It is a much stronger plywood than just any old plywood. On my 272LE I had a similar problem and repaired the bulkhead and then added ¼” steel supports to where the chain plates attach to the bulkhead to give greater strength and support to how it pulls on the bulkhead. However you decide to do it, remember that when you tension your shroud lines it pulls the chain plates upward and will cause small openings where it feeds through the deck allowing a place for water to seep in. So once you tension your shrouds, inspect your feed throughs to ensure that it is still sealed.Fair winds,Gerry