I made a setup with two 4051 mux IC's and 16 slide potentiometers. I could read all 16 pots and put the 16 values in a string and send that string out the serial port to a PC program i wrote in 10 ms. I did not try any faster but it could probably be done faster with direct port manipulation in stard of Arduinos Digital read / write which is quite slow.
I used the code from the 4051 example in the playground as the base of my work, only made a few changes.
If you need 60 pots then you would need 8 4051's that might ad some more delay than in my case.