Laser Cockpit repair

I just bought a 1991 laser a few weeks ago with a lot of nice accessories and felt I got the whole package for a good deal, however, the cockpit floor is soft. It didn’t seem too bad to me until I actually got it wet and realized how much it flexed under pressure. The deck of the boat, gunnel, and front of the cockpit are completely solid, the only effected area is the rear of the cockpit. How/should I go about this repair to stiffen it again (I fear using it this way will make it worse)...

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