What I meant by halving my bandwidth was the bandwidth of the middleman computer. I can easily read from my existing NAS at ~110MB/s, saturating my gigabit connection. If it's simultaneously reading and writing to the new unRAID box, even at only 40MB/s, it's still going to slow the whole process down.
I was able to do what I wanted to basically in reverse. From the command line in the ReadyNAS, I mounted the unRAID box, and did the copy from that end. A day and a half later, I'm done.