U can use this free Speed test http://www.totusoft.com/lanspeed1 when you Copy tracks and see the bandwidth overhead

Then the bottleneck may be the NAS and/or the network.

No, from my NAS. An old Netgear.

Are both syncing and playing files coming from a local drive?

While I sync albums to an USB3 stick I can't play music. Music constantly hampers; sounds like a badly damaged record.
I would think that the different cores of the processor would handle this.

Very annoying!