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...and I suspect maybe a plain non-RAID disk might be faster because there is no compute overhead to speak of.
Verify you are getting a GB link on all device withing the link between the DNS-321 and the PC. You may also want to set the IP address on the PC and DNS-321 static and test it directly connected. If it still does not seem faster they locking both of them to GB so it can only connect to GB and see then try jumbo frames.
I apologize for sounding dense, but how do I do all that?
You should be doing better than that. I don't think the DNS-655 supports jumbo frames, so that could actually be slowing you down. Try without jumbo frames.
It sure sounds like a link in the chain is running at 100mbit, no way you should be limited to that.
Put a gigabit switch in front of the router and connect all the devices to that switch. This will eliminate the router from the picture.