A HS-785HB is just an ordinary servo with more travel. Instead of 90 degrees of travel, it does 1260 degrees (3 1/2 turns) with a typical transmitter on a proportional channel. Depending on the particular transmitter.
Plug it into a switched channel and see how many turns you get between one switch position and the other. Once you know that plus knowing the diameter of the drum, you know the travel available. After that, its just a case of working out the best arrangements for the string, matching the travel you have with the travel required for raising and lowering the ramp. And stopping when you get there. With a 1" diameter drum, thats about 11" of travel, but the settings on the switched channel might be different.