Is there an option to define edge to surface contact for shell meshes (imagine a T like contact situation) ? You have this option for GLUE, but as I see NX Nastran does not offer such contact option.
You are correct in the context of edge-surface glue not having a general contact equivalent. Edge-edge contact exists, but that assumes that the 2D elements are very close to being in the same plane. There is a general surface-surface contact too, but that doesn't apply to your situation.
SOL 601 advanced non-linear does support node to surface contact. Don't take my word for it that it solves your problem, but I think it is worth reviewing the documentation and testing if it sounds promising. I believe you can set this up as surface to surface contact, but the source side is really reduced to nodes. Your edge elements would be the source in a surface to surface contact pair. Or maybe a better NX Nastran user can confirm that it can properly model shell edge to surface contact with its node to surface contact capabilities.
In my case I continued to use edge to surface GLUE using SOL 401, nonlinear material properties were priority for me. However as I see from your picture you have to use contact.
You can maybe try new SOL 402.