I sort of figured out a solution. Put the whole simpleTogglePanel into a div, and put the style on that enclosing div, and it works. I'm wondering if there is a better way though. Nested divs are becoming as ugly as nested tables of old.
I figured out the trick: if there is no width param specified, it defaults to width=100%. I think that is a bug. I put in width="" (literally, width is an empty string) and then it all worked perfectly. Is this a bug?