The answer isn't as straight forwarded as you would like and involved some wizardry. There are several moving parts. The first is the quality of the RTF-HTML conversion. I superstrongly suggest you give Ben a call. In case he doesn't handle tabbed tables (which are a beast), these are the steps to get a solution (I hope the force Javascript is strong with you):
Familiarize yourself with the Table handling and rendering. To do so, open the RichText field on its own in the browser. The trick is the ?OpenField command as documented by Carl.
In that HTML you can click on the various tabs to show that content, look at the URL and the source to learn about the exact syntax (which AFAIK isn't documented - or the documentation is well hidden)
By now you should have an idea how to identify a tabbed table by its HTML markup. Try to construct a Dojo selector or a JQuery (whatever is your poison).
Now show your page without the RichText field, but place a placeholder <div id="RTPlaceholder" />
where you want to show your content (or place a dijit panel there).
Use an Ajax call to ?OpenField
to get the content. With your query expression you check for tabbed tables - if none there, just render the content
If you found a tabbed table, you construct a dijit tabbed table (or a UI framework of your choice equivalent) and make one call per tab to fill them. Some clever queries are needed (you don't want the surrounding table, but only tab-label and content).
That's the general direction. So Step 1: a little chat with Ben. As usual the devil is in the details, so you need to be brave.
Memento bene:
RichText > HTML => false;
HTML > RichText => false;
HMTL != RichText => true;
Let us know how it goes!