Are you sure that what you propose with two PI loops is the way to solve this problem?

I think what you really need is to work out details of master encoder position reporting against the exact places the carriage with the saw has to be at each point in time to get the cut to happen in the right place. This is a cyclic activity that uses something I would think of as a Coordinated Motion Profile. As positions are reported by the master encoder for each cycle there will be a specific spot that the saw carriage will have to be at those same times. Think of it as a table look-up process where the length of the table corresponds to one whole cycle of the process. The sample rate that you use to index into the table can be the passage of a certain number of counts of the master encoder. The necessary acceleration and decelleration of the carriage assembly is controlled by how much you move the carriage axis for each sample period. Of course there will be a maximum acceleration that the saw carriage can support and that will translate back to the maximum rate that the line feed rate can be set to.

Any PI or PID loop you put into the controller should be put there simply to permit position control requests to be given to the carriage axis controller to keep that stable - and yet fast enough to keep up with the position control commands that you will give to that axis. The hardest acceleration to deal with will be the fast flyback of the carriage and then stopping it suddenly to turn it around for the start of the next cycle. The flyback time will directly determine how short of item can be cut off by the machine.

Michael Karas