We are using a water- based contact cement for aircraft fabric work. I am an old dude, and reluctant to change, but this new stuff is stronger than the old cement, and can be rolled off a surface where it is not wanted. It is magic, and occasionally I bring the bottle home to glue some train stuff together. Yesterday it was the soles on my spouse's shoes.
That said, I personally would carefully get some super glue in there, and apply pressure.
