Can I animate a presentation using BOTH timed and "on click" advances? Specifically, I would like to have a group of slides, say slides 1-6 automatically (timed) advance and keep repeating (1-6, 1-6, 1-6, 1-6, etc.) AND THEN, upon a click, move on to the remaining slides, say slides 7-15 which advance by clicks until the last slide is displayed.

You can do this (nearly) by creating two custom shows.

One for slides 1 - 6 and one for the remainder.

Have a button in the first show to move to the second and set the whole presentation to loop. Show slides Custom Show 1

If you wish you can make the "Move on" buttons full slide size and transparent.

DEMO HERE