single-mySlug.php works: archive-mySlug.php does not. Custom Post Type

Your setup would mean that archive-listing.php would be used at:

http://martcol.co.uk/listing/

However, your URL:

http://martcol.co.uk/listing/organisation/children/

Is not a post archive, it’s a taxonomy archive, specifically an organisation archive, and so archive-listing.php will never be used for it, since archive-listing is not a taxonomy archive template but a post archive template.

Other than doing an include in taxonomy-organisation.php there is no way to make it call archive-listing.php, except for messing around with hooks and filters, which I strongly recommend against as it would be a waste of time and effort ( why not just include ).

I recommend looking up the template hierarchy diagram and bookmarking it