An improvement that will help drogue steering (note, I'm not saying it will work well, but it will work better) is to lead the drogue bridle forward to the midpoint of the boat. This is typically the widest point and the center of rotation about the keel).
We tested the drogue with Paul before Pac Cup and found one other really important fact. Drogue steering is far more effective the faster you go. Consider motoring even if it just to give a small speed boost when there is wind.
Paul also said our drogue steering was no worse than some of the erudders he had tested. He gave the drogue a minimal passing mark for the inspection and then we installed and SOS rudder before the race start.
The drogue was a Galerider and somewhere on the interweb there is a write up a 40ish footer that removed their rudder and said they could do donuts inside the marina with the drogue because it was so effective. Hard to know how that translates when you test the drogue (or any erudder) with the main rudder still in place. Our J/120 rudder is plenty big and powerful. Not easy to overcome.