Scott, this is not a support request, I don't need any assistance. I have this working on my project using a workaround. It is a bug report. I'll try to explain in more detail:
The way that jquery.ui.tabs is designed, it's not straightforward to make your panels seperate from your tabs. For the project that I'm working on, I have 2-levels of navigation, like so:
(There's a weird issue with jsfiddle not running the second sub-tabs.tabs, so make sure you click RUN on that fiddle to see a more accurate result)
If the panels don't get a container, they will overwrite any content with the incoming AJAX request, so the "wrappers" are necessary.
Now, while this would work without any effects at all (show/hide), a huge bit of content coming in via AJAX will cause an annoying jump. The height toggle smooths out the animation. So the oldPanel gets hidden immediately (it does jump in this case), but the new panel will come in a little more gracefully.
There are a couple of ways around it, for example, I could manually animate the opening and closing of the panels rather than rely on .tabs(fx) to do that, but that's beside the point. The issue here, and thus the bug report is the fact that the fx animation will always toggle rather than excplicitly hide when the panel closes, and show when the panel is activated. So when the parent element (section) is already hidden, the animation (height: 'toggle') will not hide the panel, so the next time the panel is activated, the height: 'toggle' will fire and hide the content rather than show it... which is important for incoming AJAX content.
While the jsfiddle example is not exhaustive for every circumstance, I tried to simplify it as much as possible to illustrate the problem with the animation within the .tabs widget.
Hope that helps.