I would like to select a whole mess of notes in a track, all of varying lengths, and change them so that they're all dotted sixteenth notes. Exactly dotted sixteenth notes in length.

I don't want to change the start time for any of the notes.

And I certainly don't want to edit them ONE AT A TIME.

Can this be done?

I think Edit-Replace allows this.
You'll need to know the Duration value you want, if I recall correctly.