So, there are essentially 4 ways to write text on an image using php.
So, it would appear that I can simply set the position to relative before I mess up the layout, and everything seems to work.
This is disturbing.
Back to Image Overlay. I have decided to set the position of the image absolutely, and make the height of the tabs fixed. The text tab will have to be an exception to this, of course, as it needs so much more space. Therefore I will move the image down when the last tab is clicked.
This is getting very old. Being sick means less work is done, which means less fun.
News:
On localhost, I have the tabbed interface working - mostly. Integrating with themes will be a real pain - I need to look into JQuery UI Tabs Module and see if I can steal some code from that. I'm also looking at the Farbtastic color picker, which is included with Drupal, and studying the Color module in core to figure out how to best utilize it. I'm also considering an option to leave my simple picker in instead, although I'll need to get it working with non Firefox browsers first.