I found two solutions, one that I would not recommend and a better one which I will use next time.
Before the Whitaker workshop I bought a "Kinsey wet canvas carrier" from ASW, for about $9. It consists of two separate metal clasps that are meant to go between the two wet canvases and hold them face to face, but about a half inch apart. One clasp is for the top of the canvases and one for the bottom. It holds the canvases quite securely, but it damages almost an inch at the top and bottom of the front of each canvas, where the clips dig into the painting. I won't use this system again.
Here's what I will do next time (thanks to Carl Toboika and Craig Luzum for the idea).
I'll cut four lengths of sturdy mat board, the lengths of the sides of my two canvases and about two inches wide. (For a 16x20 canvas that would be two pieces 16" long and two inches wide, and two pieces which would be 20" long by two inches wide.)
I'll bring a stapler and staple the mat board to the sides of the stretcher bars.
Here's my sloppy, but hopefully sufficient, diagram:
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