Settings to get the correct cloth motion relative to a balloon

When a balloon floats through the air freely the string hangs straight down, perturbed only by gusts. My scene moves a balloon through the air simulating being moved by the wind. A string is painted with “cloth” and parented to the balloon. Using “cloth” on the string causes the string to flap behind the balloon like its a flag on a plane. Since the relative wind is near zero this is incorrect physical behavior.

I was hoping to get the correct effect with local space simulation on the string asset. However this has no noticeable effect. I have also set the linear, angular and centrifugal scale to 0, also with little effect.

This issue also comes up with balloon flags and parachutes.

Suggestions on how the string can be driven by the relative (local to the balloon) wind?