We've had a couple of boats with the problems you are describing.
We cut a fairly large section of the deck out around the step exposing the soaked core. Usually it's not reasonable to expect to get all the wet core exposed. We removed the core where the section was cut out and then tried to dry as best we could the rest. We used acetone and fans. Then we layed up glass to replace the core, replaced the section we originally removed and had a glass guy make it look pretty.
Make sure the compression post or bulkhead is doing it's job. Replace it or add one if necessary.
Last resort, add a section to the mast and make her keel stepped. Lots more work but no more worries about a soft cabin house.