I think I now have the Page Contents and Credits menu systems working in an acceptable way across devices. They work like this:

1. If you have JavaScript turned off, then mousing over the buttons will show the menus, and clicking on them will work as expected, except that in the case of the Credits menu, when you click on a name, you'll be taken to the page for that person (rather than seeing a popup box, which is dependent on JavaScript).
2. If you have JS turned on (the normal state), mousing over the button will do nothing, but if you click on it, you'll see the menu. When you navigate via the page menu, the menu will disappear after every click, but for the Credits menu it will stay open until you click on the button again. Clicking on names in the Credits menu will show the popup for the person.

I've tested this on desktop Chrome and Firefox, and on Android and iPad tablets, and it all seems to work correctly.

This gives us a level of graceful-failure on the menus that is far better than that in the content itself; links in the content right now are completely dependent on JavaScript.