brooke’s method is the only one that is doing what JonZ MarZ is asking about. It seems unbelievable that AE isn’t capable of moving the mask’s position over multiple keyframes simultaneously. (Highlighting all keyframes and using the cursor keys didn’t work for me either, at least not on my 2013 Mac Pro, AE v. 14.2.1.34). I wonder if it did work and broke somewhere along the way.
Thanks for finding the workaround, brooke! I needed it today!