Rendering a region in region--footer.tpl.php
as you wrote, you can override the region.tpl.php files, following the template name conventions - I would post a link, but drupal.org is down right now. A quick web search should get you to the right url and you can create a region specific tpl file. 

you shouldn't try to render one region in another, but you can duplicate the code in both region files, or of course, you could also include the code in two blocks, one for each region