I think I remember reading that the older ("classic" boats had a plywood core in the bottom, but I'm not sure, plus that might not be the 16 anyway. But, it doesn't matter that much. I'd bet dollars to doughnuts it's *some* kind of wood coring, and what you describe is a classic scenario of saturated/rotted core, as can easily happen around a fastener hole. It does sound like balsa from what you describe (my 22 also has balsa in the bottom).
The fact that you took core samples 4" out that are dry is great. Whew! Here is what I would do now (there is some variation in how different people handle these things, and more than one right answer).
1) I would want to get all the wet coring out. Now, it may not be easily possible, and the plan might change, but that would be my initial goal.
2) There is no "hard line" on this, but essentially up to a certain size hole you can just fill with thickened epoxy; past a certain diameter you would want to finish with a circle of fiberglass (over the thickened epoxy). I'd put the "line" at around 1/2" or maybe a bit more.
3) I would start by going into the holes you have and seeing how far back you can dig, and if you can get to dry core. If so, great. If not, I would drill bigger holes. You can get creative about reaching in to dig out core. I have had great luck with a dental pick, but also use a Dremel #115 bit at times, or other Dremel bits (pick is quiet and not as dusty). I had some wet core around fuel tank cleat fasteners. In the biggest spot (about the diameter of a 50 cent piece), I drilled something like a 1/2" hole and dug from there and was able to get to dry core all around. It is possible to cut as large a hole as you need to, but anything much larger you would want to patch with fiberglass, to my mind.
4) Once you have all the wet stuff out, you can fill, which will also seal the core there from new moisture. I've become fond of the WEST 610 now, but used "home brew" thickened epoxy for years too. At any rate, you first soak the area with "neat" epoxy (I either paint it on, or inject it with a syringe, let it soak, and then suck it back out), and then you go back in with thickened (colloidal silica or structural filler) and fill the hole completely. If needed, then you can glass over the top.
5) Additional notes:
-- I usually chamfer the top of the hole a bit for more contact area.
-- Make sure to solvent wash or otherwise remove dust and etc. between operations.
-- If you keep the epoxy in the green stage (easily dentable), you can just do it all without having to sand or wash between layers. If it hardens past that stage, you have to start from scratch with washing, sanding, etc. (window for chemical bond is then gone and you have to get a mechanical bond).
-- No matter how big your holes are, undercut the balsa a bit so that you have a "hook" rim on the underside of the top fiberglass skin (vs. just a smooth wall all the way up, if that makes sense).
-- With a blind hole (i.e. no outlet on the bottom) you will have trouble filling without trapping air if you fill from the top. If you can, use a syringe maybe with a straw or small shrink tubing and start filling from the bottom and going up (or connect two holes so you can do it like a lower unit).
-- Taping around everything and being tidy is a lot easier than cleaning up otherwise. I tape over the whole shebang and then use an Exacto knife to cut out the hole area.
-- If you don three or more disposable gloves when starting, then you can just a dirty one off to reveal a fresh one without getting your skin epoxied (you can get sensitized).