Solution:
This is much easier to do in WordPress 3.3 using the wp_editor() function.
I’m working on a plugin that will add a TinyMCE instance to a theme options page. Here’s what it looks like:
// Add TinyMCE visual editor
wp_editor( $content, $id );
Where $content is the stored content and $id is the name of the field. Options can also be passed to customize the TinyMCE functionality, check out the WordPress Codex for more details.