Oh my gosh this is easy, and now I feel dumb. But the answer does highlight a slight usability problem with the 3.2 version of WordPress.
Basically, WP 3.2 hides several of the options that are available to you when editing a static page. To reveal those options, you have to click on the "Screen Options" tab next to the "Help" tab at the top. By default, "Custom Fields," "Discussion," "Comments," "Slug," "Author," and "Revisions" are all disabled, which results in these sections being hidden from view.
So, to disable comments for specific pages on WordPress 3.2, using the Mystique theme (or any other theme, apparently):
Go into the page-editor for whatever page you want to disable comments on. Click the "Screen Options" tab at the top, next to "Help." Put a checkmark in "Discussion." Scroll down. Under the page-editing box, you'll find the "Discussion" options, which were previously hidden. Uncheck "Allow Comments." Re-publish the page. Done.
God, I spent more than four hours looking for this solution. I can't believe it was this easy. Now I feel dumb. Hopefully these instructions will save someone else from wasting as much time as I did.