All four instances are SQL Server 2012 Enterprise

We've configured the affinity like that because these instances used to be completely separate (but much less powerful) servers, and when we negotiated the purchase of the larger servers with management we had to guarantee that any one instance would not be able to affect the performance of any other instance by encroaching on its resources.

In other words, if someone does something crazy in NCR, it should affect only NCR. It should not be able to max out more than its 3 CPUs or eat up more than its 8gb of RAM.

Is there another way to limit which cores a given instance will use?

Jon