So far, I've been able to put page, node, field and block templates in their own separate folders. My idea is that Drupal needs to find the main original tpl file (ie page.tpl.php) in a folder and will then look for the overriding files in that directory. If so, how do I structure a similar thing for my Views templates? Do I create a few folders and put the original files (view-fields.tpl.php etc) in each respective folder?
I'll try my own suggestion and will post back if it works, so that others can benefit from it.