Servo Keeps Trying to Turn
The reason they keep trying to turn is mechanical. The physical stop in the gears is hit before the encoder/potentiometer reaches its end point.

You can make the servo stop fidgeting by completely relaxing it if you want. just use

s1.detach();
s2.detach();


and your arduino will stop sending any signal. 

Bear in mind that "reading" the value of a servo in arduino gives you the servo's current set point, not its current location. Your code in unfortunately unaware of a servo's actual location. With that in mind, setting your servo to go to 0, waiting for it to get there with a delay, and then detaching it will have the desired effect, but since it will not maintain position and you will need to reattach it to function again, using 1 or 2 as your far left endpoint is likely the better option.