I looked at the specs for this model and it looks as if the LAN ports are only 10/100. This is most likely the reason that the My Book Live is not transfering as fast as you would like. It is limited by the bandwidth of the LAN port.
Would either of you be so kind as to explain why a 100mbit connection would prevent someone from copying files to the NAS? Or why the GUI would be slow. I don’t have a gigabit switch, and can confirm that the gui is as interactive as anyone could ask for running at a mere 12mbyte/s.
The router won’t be applying QOS on the lan side.
How well is the router performing on other tasks, for example can you stream from another computer or copy files across the network (between two computers, neither of which are the my book live)? If you switch off all computers except one and the my book live, is the performance still terrible?
As a simple step, unplug the router for a while and plug it back in. Some home routers are sufficiently badly written that pushing a lot of data through one will bring it to a grinding halt until rebooted.
edit: To clarify, I’m also accusing your router. The device working well locally but not through the switch rules out pretty much everything aside from network problems.