Dear curtisF,
1. You have to assign taxonomy "project_categories" to post type "Projects". Go to Edit Taxonomy page, find Select Post Types area and click (X) Project. Than click Save Taxonomy.
2. Can you confirm that deleted taxonomies not shown on "Custom Types and Taxonomies" page (yourhost.com/wp-admin/admin.php?page=wpcf-ctt)?
Please let me know if you are satisfied with my answer and if I can help you with any other questions you might have.
Regards,
Gen.