If it only happens while copying files to your NAS, it is most likely your network. I am assuming the PC is on wired ethernet? (I saw that the NAS is). If not, wire it. And make sure the network adapters are all on full duplex.
I have seen the drive get bogged down enough to make video playback stutter when copying from a green drive over 1Gb/s LAN to a much faster PC/drive pool. So it is possible that you could have a disk bottleneck within the NAS during the copies. Or it could just be that the NAS has an inadequate CPU to handle the copying and streaming simultaneously.
It's cat 6 end to end, all gig-e. My HTPC specs are:
Corsair HX850W PSU
Intel i5-2500k CPU
ASUS P8P67 Deluxe Motherboard
2x4GB G.SKILL Ripjaws PC1600 DDR3 RAM
Gigabyte GTX-470 Super Overclocked
Crucial C300 SATA3 64GB SSD
WD Caviar 7200RPM SATA3 1TB HD
So it's not the most powerful gaming rig ever built, but I'm not exactly worried about its performance.
Given than the throughput of the ReadyNAS is 36MB/s, I'm absolutely convinced it's the bottleneck. There's no chance I'm saturating my wired gig-e network.
Looks I'm going the FreeNAS route! I've never built a low-power system before, so this should be interesting... I understand with ZFS RAM is king, but not sure where to draw the line with processor power or how important that is, if the intel/amd battle matters (I think I read FreeNAS works better with intel ethernet chipsets... Do you just run FreeNAS off a flash dirve, or is it recommended to use a dedicated hard drive? I guess I need a motherboard capable of supporting my 4 array drives (+1 if I use an OS drive). What about power supply wattages?
So many options! And that's before considering anything like LAGG? Which I know nothing about...