The strongest glue for what you propose is 3M Super Weatherstrip Adhesive, known affectionately as "Yellow Peril". It is a single part contact adhesive with good flex. It is called "Yellow Peril" because you only have one chance to get the parts to be joined straight. If you missalign them, that's it. It will not release. There is no repositioning time. But when you join two things with it, they are joined until the sun goes out.

The second choice is what shoe repair shops use for attaching soles - a rubber-based, single part adhesive. Barge's Cement is probably the best.

In both cases, make sure the parts are super clean and then whack them together with a mallet after joining them. That is a very important step to insuring a good bond.

Goop and Shoe Goo are the same thing. They will peel off.