Like I say, I am not aware of any mechanism that allows this.
Yes, that might be the beginning of a mediocre idea, not that my similar one was that much better. I wonder how much extra tether you would need for this. Say you want the loop to have a length of 200 meters but to get to that length, the airborne pulley needs to rotate for a minute at 20 m/s, which would unwind 1200 meters of tether from one drum. The other drum would also not stay static during that time, reeling in instead, slower than the other drum is unwound, also adding some, but less, tether length to the rope drive, so you might consume 10 times as much tether as you need. Then at the end, still one end the tether is still partly wrapped around a drum. So I don’t know how that would work.
Another idea would be to now add an extra drum next to the loop, rotating at the same speed as the tether, with now an extra arm adding wraps around this drum, like how you would reel in a kite by using one hand to wrap the line around a drum in your other hand. This would work I think, for short lengths. This extra drum could also replace the ground station pulley.
I remember seeing a YouTube video around that time, probably linked on the Yahoo forum and since disappeared, where I think I remember the balloon deforming from the torque the balloon placed on the generators, or maybe from their weight. My memory is fuzzy on it collapsing further. The two videos I could find now don’t have the generator attached and have just the balloon spinning freely. Someone like @dougselsam might have commented they should have connected the two generators together with a pole.