I agree. And one possible old-school trick from back in the day is to use a partially-inflated ziplock bag. We used to mix up (as my aussie friends used to call it) a "pot of bog" - thickened epoxy, to a consistency of putty with a little "slump" to it - slather it into the gap, and then shove a partially-inflated ziplock in behind it. If you do it right, the ziplock bag will wedge into the gap and provide a bulkhead, of sorts, holding the epoxy into solid contact with the core and the top/bottom skins until it sets. Once it is set you can pull out the ziplock bag and know you have a solid surface to work against.Use regular neat epoxy and just paint it in with a long-handled brush and a prayer
May or may not be appropriate in this circumstance, but a useful trick to have in your bag.