I presume when you manually apply the trailer brakes the sway goes away. Here is something to consider: There is always a little slop or play form the insertion of the shank into the receiver. Since you used a shank with a longer drop the side to side play will be magnified. It could be the looseness in this joint is causing a slight movement of the hitch ball in one direction, then over correction then movement in the other direction, over correction then sway.
They make a heavy duty clamp available from Amazon to reduce hitch rattle. Essentially it securely clamps your shank to the receiver. Mount it from the side instead of vertically. For 16 bucks it might be worth a try.
