That engine exhaust is probably the bane of J/30s. On my boat (#205), it was simply an aluminum pipe stuck through the cored transom. A little bedding trown around the edges to keep water out. Not very effective at that.
I've removed the aluminum tube and replaced it with a proper HEAVY brass exhaust, removed the soaked core around it, and filled with epoxy. Water WILL NOT get into the core from that hole anymore.