If you can remove the headliner you can drill holes from the bottom to check the extent of the damage. If the core is wet to a small distance out, but not rotted or delaminated from the skins, mount a heat lamp below to dry out the core. Then refill the area you have already dug out with epoxy. My approach would be to seal all the holes/slot with tape from below and fill the slot with some epoxy to wet things out (probe with a long nail to make sure everything gets covered) . Remove the tape from the slot to drain the epoxy, then mix a batch of thickened epoxy (colloidal silica) and pack the deck taking care to eliminate voids as best you can. Small voids are not a big deal unless they are pervasive. Use a slow hardener. Finally fill the drill holes from below with thickened epoxy and add a layer of fiberglass to strengthen and seal things up.
If the damaged area is not too large you could also consider replacing the slot coverplate with a larger stainless steel plate to cover a repair done from the top. Should look okay. If the rotted area is large you will be faced a recore job from the top or bottom.