Thanks for the suggestions everyone.
Jeff, you're right about the cost of the Dymax UV adhesive; it's a large fraction of the cost of the TV stand!
Jon, I had considered quick set epoxy, and probably would have used it if one of the joints wasn't visible. Thanks for the warning.
I think I'll use the Gorilla Clear adhesive. The online reviews look good and I can get it locally, so the job can be done quickly. I wouldn't be popular if the room was repainted for Christmas, but the TV was balanced on a chair!