I'm interested to hear what others have to say, but a soft floor to me indicates a larger issue. You're obviously holding water in there, and I shudder to think what it looks like under the floor boards.
I've dealt with lots of boats way older than that with no floor issues. If it were my boat, I'd pull the floor up, fix whatever you find, and put in new floor and carpet over the winter. If not, problem will only get worse.