I wouldn't make this any more difficult than it needs to be. You have convenient access right in the middle of the sponginess, so use it.
Remove the fuel fill and scoop out all the rotten core around it. Let it dry out. Seal the bottom of that big hole with duct tape or (what I used) a carefully-laid piece of 5-minute epoxy stick -- the putty kind. Then fill up the whole darn thing with thickened epoxy, a few ounces at a time so it doesn't catch anything on fire.
Once solidified, redrill the hole for the deck fill and put it back in.