Bent coathanger does it all.
If the rod fitted in a hole 'drilled all the way through' the body of the plane you wouldn't have to worry about icing etc. as it would be protected.
Why bother with the rod at all? It doesn't do anything for directional stability in the fraction of a second it takes for the plane to be popped off by the rocket.
I'd take a coat hanger, cut the horizontal bit and form two elbow hooks to go under/behind the wings. Tilt the hooks so the plane points up, dangle from a string and off you go. No beam even simply tandem balloons.