I'm big into RC aircraft and ran into Ultimate RC Foam Glue a long time ago... it's awesome stuff. Until it was discontinued that is (major sad).

A friend of mine suggested Beacon 3-in-1; it turns out that it has many of the desirable characteristics of URCFG.

It comes out like normal glue.

It can get a little stringy during application - make sure that you cover your entire surface with a thin coat.

Here's the trick in application.

Press the two parts together lightly, then pull them apart two to three times - until you can feel the adhesive resist being pulled apart. You may need to blow gently on the glue a bit to help things along.

Now, press the parts firmly together; you can make small adjustments for some time after.

Glue a few segments at a time, leaving them to dry / cure for at least an hour between. The final result will be strong but slightly flexible.