I went to current board settings and changed the theme to YAF Pro (as well as several other themes), but it only changes the entry page theme and none of the topic pages.

How do I change the theme for the rest of the pages (instead of only the index page)?

I had used the "So Fresh, So Clean" theme and the topic pages are stuck on that theme. Refreshing the browser or clearing the cache does not help.

It works on another of my forums (identical code & version, no customizations)

It should be taken care at the time of designing the homepage and other respective inner pages on the website. It is so important to maintain the uniformity of the website theme.