Git Rot IS epoxy, only thinner than the West Systems stuff, so once you dry out the core it will soak up into it better. It really isn't necessary to remove the rotted core, except in the area of the hinges where you need to have screws, which should be filled with thickened epoxy.
As much as I dislike Griviskas for his superficial coverage of stuff and shameless promotion of whoever gives him free stuff, ShipShape TV did have an outfit on a couple weeks ago called
Dryboat that you might be interested in. They had a big Clorox bottle shaped boat that used lots of cheap foam instead of fiberglass in the hull construction that was full of water. They drilled a bunch of drain holes along the chine and then used a vacuum system to suck the water out of it. I'm sure it's big bucks but maybe worth a look if only to convince yourself how much $ you're saving with the DIY approach!