I believe you know this is going to be a PITA. However keeping on task with the objective I would work from the bottom, cut the section out as best you can that is soggy, provide a reasonably smooth surface to attach 3/4 marine plywood that you can epoxy (thickened) to the underside of the deck using a notched trowel ( you may have to use pieces that you can fit in there and dowel or plate join them together) then over lap the seam with another piece of ply screwed and glued. If the deck has curve to it you can use 1/4" wood that conforms better to the deck and laminate it to desired thickness. if you feel the need reinforce with gussets' or just coat with epoxy. In the end you will have a solid deck that should be more than adequate for the support you need for your rod holder. If a BFT rips the deck off let me know where you were when you hooked him and I will be there trying to catch his brother LOL
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