Is there any way to make it so only folders show the "Captions"?

You know, I don't think there is at the moment.

However with the settings in Preferences, you can chose only to show Title (and Favicon) on Hover, which keeps the Title out of the way until needed.

But this is a global setting for all cells

I suppose a possible alternative might be to use descriptive Folder Logos on your Groups/Folders, and so not use Fast Dial titles at all.

Many thanks