Hi Kristin,
I can not duplicate same problem in my localhost, are you using latest version of Views?
And I have create a test site for you, and send you an email with login details:
Here is what I create for you:
1) add a post type "type 1s", enable the page-attributes checkbox under Display Sections settings:
http://luo-1099-tb-1.discover-wp.com/wp-admin/admin.php?page=wpcf-edit-type&wpcf-post-type=type-1
2) add 3 posts, set each menu order as 1,2,3
http://luo-1099-tb-1.discover-wp.com/wp-admin/edit.php?post_type=type-1
3) create a View to list post order by menu order:
http://luo-1099-tb-1.discover-wp.com/wp-admin/post.php?post=41&action=edit
4) put above view into a page:
http://luo-1099-tb-1.discover-wp.com/order-by-menu_order-not-working/
You can try alter the order of step 3, and test