It took me a while, but I figured it out. Turning off all caches internal and external did fix the issue, but then turning them back on, even when clearing them, brought the issue back. Finally, by turning things off one at a time, I figured out that the problem is with the minify cache in the Wordpress W3 Total Cache plugin. Turning that off makes the accordions work, turning it on prevents them from working. All the other caches, both in W3 Total Cache and the external cache optimization service work fine. Clearing the minify cache specifically also did not fix the problem.
For now, I’ve left the minify cache turned off, but I’d really like to be able to turn this back on, so could you please submit this as a bug report? Thanks.