Can I use a custom post type as a custom taxonomy for a different custom post type?

The plugin CPTonomies is designed to exactly this. There is no built-in WordPress way to do this.

I’ve never tried to make WordPress do this, but this is the plugin I’ve seen used by others trying to achieve this functionality. You might also try Posts 2 Posts, which creates relationships between different post types instead of doubling a post type title as a taxonomy.