I have never been fond of the sideslip cards, but the other day I had an idea which made them more palatable to me. What if they were dependent on which tack you were on? If you were on a port tack and played a starboard sideslip the movement arcs would be reversed and vice a versa for a starboard tack.
This would have the effect of speeding up a ship going to windward but not allowing it to point as high, and slowing down a ship turning farther downwind, just like the dead downwind arc on the back of the base.
The effect of both of these maneuvers are often seen in sailboat handling these days.
Port tack with a turn to port and vice a versa would be played as written on the card.