I've found the solution! Thanks to this post: http://wordpress.org/support/topic/67016
In archives.php, replace every instance of "the_excerpt" with "the_content", as the above post says to do.
BUT also replace every instance of "post_excerpt" with "post_content".
By doing BOTH of these things, the password box will show up in both the category and single-entry views. The password-protected post itself will not be visible.
Hopefully this is something that had already been figured out... but if not, I'm glad to have shared the solution :)