Just an FYI and addition to the email I sent you. As another test, I changed my import to be a standard post instead of the custom post type, and did not import any custom fields. But I used the same data for !post_title, !post_name, !post_status, !post_type, !post_author and !comment_status. I still had the Types – Complete Solution for Custom Fields and Types plugin active., but all other plugins inactive.
After this import I could see the post in the webpage for the Uncategorized category.
So the issue seems to revolve around custom taxonomies.