Having worked with subs, mainly with twin screws. Transfers with all RN subs on the move is done on the forward diving plane, so that you could steam in the same direction as the sub and veer away. You would never normally go along side of a moving sub, as when you would normally increase speed veer off, your screws with a sub will make contact. The sucksion of the subs screw can pull you in and also when you back off, the tug has to stop and twist it's stern out and so it will move down the hull as the sub moves ahead. I was in a similar postion many years ago when a dog I was on had a M/E failure and I had to get off a moving sub on one screw, not to be reccommended.