Reviving this thread from the dead to mention the solution my wife and I found.
Basically, we have the extender sit vertically between the table leg and the rotating table support bar (that holds up the other folding half of the table when it is deployed). With the correct size bungee, it will put just the right pressure on it to keep it in place in the vertical direction.
The forward-aft horizontal motion is prevented by the table leg and the rotating table support bar. The port-starboard horizontal motion is prevented by the rubber stop on the extender...it remains trapped between the table pin (that locks it in place during transport) and the rotating table support bar. See attached pictures...hopefully that will clarify what I'm taking about.
The only disadvantage I see to this setup is that the chrome plates for the extender pins might rub a little on the rotating table support bar, but that could easily be remedied by a couple pieces of electrical tape IF it is even an issue (we haven't had any problems yet, so it may not be).