What is the link to your site? You can see this in action on this page - hidden link
Below the main content but above the Instagram block.
My issue is that, if the post is in more than one category, the link shows them all. Is there a way to use just the Primary category, or even just the first category that the system finds?
This is actually an easy fix, what you need to do is create a view, a taxonomy view that is listing out the current taxonomy for the posts.
To do this add a Taxonomy Term query filter to the view and set it to display for the current post or page or view, whichever is the one you are using to display the post.