Re: Rods are out. Rails are in.
The effect you describe is called weathercocking (which is comedic gold, but I digress). It’s described in this handy NASA bulletin: http://www.grc.nasa.gov/WWW/k-12/rocket/rktcock.html
This will not be an issue for LOHAN. As you mention, balloon airspeed will be negligible. Also, weathercocking depends on extremely large tail fins and does not happen appreciably with airplanes whose major airfoils are the wings mounted amidships.