Created a Block of 'Unrelated' Nodes There are plenty of articles on creating 'related content views', but what I need is a view of all content tagged with different terms of a specific taxonomy.

I've tried creating a view with the Taxonomy Term ID Contextual filter set to Exclude under 'More', but I'm still getting related content.
This sounds like the same question I asked here, and for which I got a "sorry, can't do" kind of answer:

How can I show a list of terms from a specific vocabulary that are not assigned to the current node

What you'd be asking SQL to do is check every term in the vocabulary to see whether it is assigned to the current node. The performance overhead of that is potentially huge (imagine a vocabulary with hundreds of terms, and a node with just one of those terms assigned).