I did it! Almost entirely by myself, with just a bit of help from Mark of Weblog Tools Collection, I widgetized my design. I now have 13 instances of the King Text plugin running, each containing the code from my original sidebar. I was not able to find a way around the problem of the title falling inside the widget, so I had to stick with modifying the plugin code, but the King Text plugin accepts both PHP and HTML so I can put whatever I like in there. If I want to add additional widget plugins, I will have to edit those too, but for now I got everything running how I want it.
I did have to make one sacrifice: the sidebars are now fixed-width rather than liquid. This is because the percent sign I was using for the liquid layout was getting tossed out by the PHP running on the plugin. It’s not a huge deal, I can always adjust the width if necessary, but it isn’t quite perfect.
But damn, I did what I want, how cool is that?!