Display a grid of taxonomy terms at root taxonomy page

After researching some more I’ve given up trying to use the taxonomy template and opted for a plugin to amend the permalinks. I followed some of the advice from this similar question: Taxonomy archive with same slug as custom post type?

Currently I am using an amended archive template for the custom post types and then the WP Better Permalinks plugin to rewrite the permalinks how I need them i.e. example.com/custom-post-type/custom-taxonomy/post-name/

If you need a simple solution this plugin works very well as far as I can tell. I also used Custom Post Type Permalinks which gives a greater level of control (this works the same way as the default WordPress permalinks settings, in that you can arrange the permalink tags in whichever way you like). The only reason I dropped this plugin is that it refused to work with one out of my five CPTs, even though everything was setup the same.

Hopefully this helps someone else in the future.