Since the AM RAW box already has the encoder mount for the E4T, you might be able to add a limit switch or hall effect sensor somewhere else on the mechanism to give the encoder a reference point. This way, you can use the encoder for absolute position. We used this approach on our 2015 elevator and it worked perfectly.
Another option is to use the AM String Potentiometer and attach it to the base of your robot and the string to the mechanism:
http://www.andymark.com/product-p/am-2674built.htm