Hi,
is the category option that is causing you issues maybe this one: blog_selected_category_id?
The issue with the category import might be, that when importing the content, the category gets assigned a different category ID, then in the original export site (the .dat file). And then, when the customizer settings are getting imported, the ID does not match to a category and that’s why it’s not set correctly.
WP assignes ID from the same pool of IDs (incrementing number : 1,2,3,4,5…), that’s what is causing the issues.
Take care!