It's good that you listed all of your FieldPoint hardware, but which of it is relevant for this issue. From what I can tell, and please do correct me if I'm wrong, is that the FP-Quad-510 and FP-PG-522 is of relevance. You determine the location you want it to move to, and you then start the pulse generation according to the reading from the FP-Quad-510. Is this correct? The problem isn't the quadrature encoder measurements, but the pulse generation.
Does the position change ever stop? How do you currently have it programmed such that it knows to stop at a certain position. There is a command used for the FP-PG-522 which will stop it's pulse generation immediately or on its next pulse. Page 8 of the FP-PG-522 Operating Instructions
The Control command supports two actions: Stop Immediately and
Stop After Current Pulse. Both of these actions can stop a finite
pulse train. Stop Immediately stops pulse generation immediately.
The channel goes into the idle state, and, if the output for the target
channel is on, it is turned off. Stop After Current Pulse ends the
current pulse train after the current pulse is finished.
Let me know your thoughts, questions, and comments.