Rob - my two cents since I had the exact same problem on Rhapsody. First - you need to stop the source. Start at the transom. Cut the outer skin starting from around the exhaust tube and incrementally work your way up and to the port side until you reach dry balsa. My stbd backstay chainplate had mush for core so I had to go to the top. I know it sounds like a lot of work, but you could recore this area yourself, and leave the finish work (final fairing and painting with Gelcoat or Awlgrip) to a pro if you are uncomfortable getting a factory finish.

When the transom is recored, you need to isolate with epoxy any bolt holes and the exhaust tube. You also should create a barrier between the transom and intersection with the core on the side and bottom of the hull so moisture can't spread.

Finally, the core replacement in the bottom can be done after the fact, and most from inside the boat so gravity works with you. I've seen some posts on drilling holes and leaving core open to dry, but I'm not convinced it is all that effective.

I would recommend to at least get the transom done as soon as possible to stop the source.