I have this same issue. Mac OS X Sierra, and I'm using a Synology NAS, where I'm reading various formats of music files and trying to save them to a different directory in the NAS. I definitely have user read/write permissions set up properly on the NAS.
The NAS is mounted via afp (Apple Filing Protocol) as per Synology instructions.
Saving 1 file at a time seems to work
Saving a single album together, or group of files, causes the program to hang, and causes my CPU to spike above 50% activity. I've force quit before, I'm currently trying to save 10 files at once, and it's hanging.
I will post back if I figure anything out.
I may try mounting via SMB2 or Samba next, instead of AFP, if that's supported. We'll see.
Failing that, I'll move the untagged files from my NAS to a local drive, or even a USB drive, and try again that way.