Removing slack from the rudder lines may help directional control, but the main benefit is improved turning radius. Slack lines don't allow the rudder to deflect to its full capacity.
Going from the small to the large rudder also helps your turn radius, but its most significant contribution is low speed rudder authority, giving much better directional command over your boat. It also greatly reduces the need for frequent corrections as you noted. and reduces response times.
I raced behind a guy in another Adventure once out in the ocean. He had a small standard rudder and I had the large sailing rudder. The swell was moving his boat around quite a bit and he was continually wagging his rudder back and forth to hold course. I think this took a toll on his speed. My boat tracked much straighter. Despite the larger surface area, there is little doubt that the large rudder's straighter tracking with fewer rudder corrections was an advantage.
I like to see a little tension in the directional lines. This helps hold the rudder in position. So far, I haven't experienced any fray or other damage. BTW, the boat expands slightly in warmer weather, making the lines tighter. IMO, this is normal and not an issue to be concerned with.
