I was able to include the individual products posts without issue(they are custom posts). However none of the categories are being added. I believe Woocommerce is saving product categories as custom Tags.
Here is an example of the end of a url to edit a category. I think this should give you the information you require
edit-tags.php?action=edit&taxonomy=product_cat&tag_ID=68&post_type=product
Also, the ability to set a different priority for custom posts (and tags in the future) would be great!