I'm working with this css template here: http://www.mycelly.com/css_templates/css_template_07.htm
I want the center content to load before the right-column content.
But if I rearrange it and list #content before #right, it gets out of whack, like this: http://www.caught22.com/load.php
Well your link doesn't
Well your link doesn't appear to load so can't tell what you may have done.
For your requirements you need to do a google search for 'Source ordered layouts' which will give you some guides to laying out content before sidebars.
As for the template I would avoid it , it will be possible to source order and quite simply as it uses position:absolute for the sidebar position so you just need to ensure they come last and that content is not widthed but given margins to pull it away from the sides. Problems will occur though if your sidebar heights ever become longer than the content.
Source ordered layouts was
Source ordered layouts was just the tip I needed.