Thanks to everyone for the tips.
I found a youtube video in which a guy did a fairly well-designed empirical assay comparing various commercially available glues to one another on their ability to keep 3D-printed PLA parts together, which you can view here.
The take-home from the video is summarized in the following chart. Below that is the winner of his head-to-head comparisons, which turns out to be regular old Loctite Ultra Gel Control Super Glue. Haven’t tried it myself yet, but I will be buying some soon. If I have any contradictory experiences, I’ll let you all know.