So, I had said in the previous thread on this that the effect of pressing A immediately after a souped anti-air depends on the timing. As it turns out, I was almost completely wrong.
On the happier side of things, I've discovered exactly how the move does work. The cause for the different effects is the direction in which the control stick is held. Once the move hits, the opponent is launched along the floor in the direction of the control stick. The speed of the launch dependson how closely the control stick matches the direction Gingy is facing, with the launch going further the more forward facing the stick is placed. I don't know exactly how the speed varies, although a decent guess would be to take the standard launch trajectory as a vector and add it to an equally sized vector in the direction of the stick, and then taking the magnitude of the result. EDIT: I am fairly certain that the speed does not vary meaningfully depending on direction, and that the backwards input dropping at Gingy's feet is a result of the opponent colliding against him, contrary to what I previously suggested.
A good consequence of this is that pulling the stick in the opposite direction of Gingy drops the opponent in blue-stun right at his feet. Whilst his follow-up options are somewhat limited, there should be enough time for a quick B-aerial, which if you shield drop after hit could be turned into another grab.
(For anyone worried about the title, I've been calling this move the "farq-off" [keeping it family-friendly]. If you're confused, just see it in action, it fits it pretty well. )