If the remaining balsa lamination is still good on your 4” rim you could go with approx 6” wide by ½ to ¾ thick plywood that you epoxy under the 4” rim with 3” supporting the old deck and 3” supporting the new deck. You would need to coat the wood first with epoxy allowing it to soak into the wood first I would also do that to the edges of the balsa wood on your 4” rim. I would also try to add one layer of glass under there as well. If you use thickened epoxy it should stick even though you will be fighting gravity under there. Make sure you ruff up and then clean up with acetone the bottom of that 4” rim before you start trying to epoxy anything down there.
FellowShip
Just for the Grins