Well, I just got back from the welding supply store and came back with another glue. The stuff is called Lab Metal and he said that it is stronger than JB weld and that it would probably work good for this application. Seeing as I have never actually brazed anything before and this would be my first shot at it, I'm going to try the super glue first.
I am not looking forward to chipping off all that JB weld though!