the servo gain was added for boats that could not get the gains high enough, or wanted to reverse the direction without rewiring.. so it's not usually needed to change for most users, you can increase the other gains.
You may benefit from making the servo gain of 1.5 or 2, but again this is basically the same as increasing all of the gains by this proportion.
If it struggled to make the new course as you describe I suggest:
1) increase P gain, if you overshoot too much, increase D, DD, and/or also increase PR while decreasing P
2) increase FF gain, so it gets a larger initial correction to changing course
3) maybe you already read my guide, but review:
https://pypilot.org/wiki/doku.php?id=tuning_gains
4) more patience, maybe?
check the servo.min_speed and servo.max_speed and servo.period settings and let us know what they are set to. This can affect performance and the trade off of noise vs power consumption vs responsiveness.
How long does it take the motor to move the rudder from stop to stop (hard over time) ? If it's longer than 6-8 seconds on typical boats anyway, then the autopilot will not react very quickly, and it may actually consume more power than a faster motor as it constantly corrects in difficult conditions.