Issue is fixed.
It was caused by an rogue .htaccess file in the installation that prevented the plugin’s JS/CSS resources from being loaded by rewriting to a URL that didn’t actually exist on the host. My fault for being too clever and then not clearing up behind myself.
I’d like to thank Pär for his swift assistance – he really took the trouble to take a close look at the setup and diagnose the problem.
Simply awesome support!