oakes, go with a better servo, get a one of futaba's better servos, they will set you back a bit more but they will work a whole lot better.
there are digital servos with extremely high resolution and repeatability and in most cases you get what you pay for (i work extra in a local hobbystore ) and and the dirt cheap ones are not good enough for what you are trying to use them for...
BTW, Sailwinch servos have 360 Degree rotation, eliminating the need for gears/point of failure but they are big and expencive, a ok digital servo will set you back from 250-300 to 1500 sek. (the 250-300 kind will do :) )
Awsome work by the way, you even got the sound of the buttons right :)