Well, here is what I did. My old super glue dispenser was dried out, as was as my only open JB Weld. Not wanting to open a fresh package for such a small job, I checked my Gorilla Glue, and found it still serviceable, so that's what I used.
I had shied away from Gorilla Glue because of the way it tends to foam out of the joint as it sets up, but I took care to use only two small drops, and have not seen any foaming at all. If this forum has taught me anything, it is how to improvise and make do with what is at hand. Thanks for all the tips.