Although not a single board table, I still intend to reproduce in my lifetime a table a friend of mine made years ago, he called it an Irish wake table-just really a longish(6-7 feet) oval drop leaf table made up of 3, 18-19 inch wide boards with long rule joints joining the three planks and 8 (4 swinging)cabriole legs for the support.
Anyway, he used what I thought was a pretty ingenious method to guarantee there would be no cupping across the grain on the two "floating leaves". On the underside of the table, he had cut 2 or 3 long sliding dovetail channels cut across the grain, into which he had slipped waxed dovetailed "sticks" or "strongbacks"into the slots to resist any tendency for the wide plank to cup-then the ends of the dovetail mortise are plugged.
I liked this method so well I have used it on some 4 foot long drop leaf tables I have made, so those free floating leaves will surely stay still. I even used one on a handkerchief table-it has a 19 inch wide floating leaf.
Make sure the plank is well seasoned(3yrs like mentioned above is really necessary), be very skeptical of any kiln-drying, put two of those sliding dovetails across the grain, and I will guarantee it will behave.
I can post a picture of the underside of the handkerchief table leaf, if desired.