I've been searching for a way of making my index page display all my subalbums, and only my subalbums. Never the parent album. Any ideas?

Try the code I posted here within the next_album() loop: http://www.zenphoto.org/support/topic.php?id=4143#post-24735
But you first should get familiar with zenphoto themes in general by reading our theming tutorial.

Thanks for that, I think that will get me on my way.
And thanks for zenphoto!