To add to db's good thinking, you could squirt it in there with some pressure...something like a pastry bag, etc.
I'm just flabbergasted as to how it hasn't gotten soft underfoot yet. Same thing with my deck, wood was rotten under cooler seat but deck felt solid. Another funny fact, the fiberglass where my gunwhale rod holders are is cored with some seriously thick wood. I should take a picture of it. Absolutely no point in that whatsoever.