I'll give a second vote for gorilla glue. Have been using it for years to join wing panels with zero failure.

The only thing I would add is to use the woodpecker also. The dents in the wood act like little rivets when the GG kicks and adds a tremendous amount more surface contact for the glue.

You will need to do a very good job clamping the panels together, that foamy action will push the pieces apart if you aren't careful.