Andy
you are correct, the interface actually uses department IDs behind the scene, not department names - it makes for a much more efficient query behind the scenes and more importantly, allows users to rename their departments without causing headaches all round.
I am thinking that one way to handle what you are looking for is to add a new field Item Department Name which would allow REGEX to run against it. The issue that arises is that the query on the back end would end up using LIKE %DEPARTMENT_NAME_FRAGMENT%, the man behind the curtain might not be best pleased.
This would be a custom dev. [ Of course a smart person like you could also map their department names into a custom text field using a NscSync mapping and then run a REGEX against that custom text field in the carousel builder interface 
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EDIT: I had a quick look at your mapping to make sure you had a free custom text field. You appear to be only using 4 custom text fields. You know there are 20 of them available in the product table?
Regards
James