I have now played around quite some bit more and find that if I disable the plugin that the site uses for running menus (Multi-level Navigation Plugin for WordPress), the Splash plugin works as expected. Even though this means I can’t use the Splash plugin without major surgery to my web site I will mark this topic as resolved. Sorry for the bother. I would also point out that the plugin that I am using is obsolete and no longer even supported by its developers. I probably should convert to using the native menu WordPress Menu system, but it won’t likely be trivial.
