The other trick if you have CA and accelerator is that you can use the combo like contact cement. Put CA on one surface, and spray the other surface with the accelerator. Press together, and they’re stuck, almost instantly.
I was cutting dovetails in some oak this morning, and ran into a void like you have, plus some punky wood. Thin CA to the rescue. I soaked it into the end grain where the wood was punky, and that firmed it up some. Also filled the void using the sawdust from cutting the dovetails and then soaked it with the thin CA and a zap of accelerator. Looks good as new. No photos though, since I was making good progress.
Fun thing was that I got the CA fumes / smoke coming out of the punky end-grain. There was something in there that was causing the CA to set almost instantly, similar to what happens if you dribble it into aluminum powder or baking soda (check out
Adam Savage’s superglue video for more fun).