Custom Columns are blank, not displaying custom taxonomy's terms

I’m fairly new to WP and have been trying out (with some success) Custom Post Types and Custom Taxonomies for building a portfolio site. But I had to change how my posts were “tagged”. Here’s the set up:

Originally, 4 CPTs (Designs, Illustrations, Paintings and Prints) and 1 custom tax called “Portfolio Type” that was shared by all of them. This would allow me to specify terms like posters, logos, ads, etc. I then updated functions.php so that each CPT could have custom columns to display these terms. Everything worked great until I realized I had to change things around.

Still the same 4 CPTs but now each has its own custom taxonomy (Design Types, Illustration Types, etc.). I did this so that terms like ads and posters wouldn’t appear under Illustration since they didn’t apply and made things confusing.

After that change, things are still working as they should except the custom columns for all but one CPT won’t display the terms associated with each post. I can still add and manage them, tag posts with them but they just won’t display, as shown here.

Since I already had a tonne of content tagged, I didn’t want to go back through the 100s of posts and re-tag everything. Instead, I backed up the database and jumped in to see how things were set up. In the wp_term_taxonomy table, I manually changed the taxonomy names to match up with the new custom taxonomies. That is to say, everything used to be under “portfolio_type”, now there’s a mix of 4 different types, as you can see here.

Is there another place in the database where I need to adjust some sort of taxonomy/term relationship? I’ve searched but I can’t find anything obvious.