I'd baste with Elmer's Washable School Glue. When I do that, all three layers stay firmly together all over.
Some people thin the glue, but I just put two bottles in a bowl filled with hot tap water. The tap water makes the glue thinner, and it comes out like spider webs. When the first bottle cools, I switch it to the second bottle and freshen the bowl with fresh hot tap water. This is the quickest way I have ever basted.
When finished the glue dries very quickly. If it had been thinned, it would have taken longer to dry.