I'll have to drop by Home Depot and see what type of moisture meter you got is there a model number? I see a number of them on the web site.
Yes, removing the top layer is a viable way to start the repair. This apparently is not structural (like the hull or an area of the cockpit floor which you step upon). It is not unusual to cut the top layer of the fiberglass around the edge where you want to remove it. A Fein or Dremel saw will do this well. You can use a router zip router or dremel tool router. I find that the Fein or Dremel (Harbor freight has a cheaper version available)--this allows a very thin cut, and not very deep. The standard router will work, but you have to use a carbide bit--and it will make a considerably wider cut than one of the saws.
I would peel off the top--using a sharp chissel or "slick". working under the top glass would be the way to go. You can determine how much wet the core is, and if you can dry it with heat and air (our experience is that just air takes a very long time, and is less likely to get it dry--if you can use a dehumidifier and seal the area with plastic, this will help to lower the humidity and make the drying process faster. You have to drive the moisture out of the wood. What we don't know is how much penetration there is into the balsa core itself (penetration of the wood cells).
You can try the half the balsa if you want...it will be a trick to get a clean cut with a router on wet balsa. I would remove all of the balsa--and put in new balsa. Yes, you can put in a solid laminate--but this will be much heavier--and use a lot of glass.
If you save the top piece, you may be able to "glue it back in" with epoxy--and then fill the edges with polyester and then gel coat these edges if necessary. If you don't want to gel coat (cosmetic)--then use epoxy all of the way around. Epoxy gives much better bonding. If you were rebuilding a hull, then I would suggest that you cut a 12/1 scarf around the edge and relaminate at the 12/1 ration--for a strong repair.
Yes, putting up photos will help all of us--as well as you.