… Is there a way to globally change all of a given chord symbol suffix, regardless of the root? …

Chord suffixes are document specific.

By your word “globally” you mean “everywhere in a specific document” - right?

I would - in the Chord Suffix Selection - select the unwanted suffix, and click the button {Delete}.

Finale will display a warning, and offer to, everywhere in the document replace the suffix with another suffix.

Thanks Peter.

Yes, I meant globally within a given document. I have several different minor chords with different extensions— min6, min7, min7(b5), etc.—and was hoping to change just the "min" and leave the extensions. I had thought of what you suggest and tried it, but it appears that the suffix that would be replaced would include the extension, not just the "min." I was hoping there was a way to search and replace just the "min" without affecting the extension characters. I suppose there aren't so many different minor chord types that would be onerous to delete and replace each of them separately. 

After you’ve done that, save a library of the chords. Then, you can use them in other documents.