How do I transfer files fast over two network shares?
Moving files from one share on a host to another share on the same host will always be faster when initiated from the host itself, and will always be slow when transferred from the host to a client (and back).  Regardless of whether you use Finder, or mv or cp or Carbon Copy Cloner, if the data has to traverse the network, it will be orders of magnitude slower.

There are some technologies that allow a copy or duplicate command on the same share to be initiated by a client and performed server-side instead of copying the whole file down to the client and then back.  I believe SMB supports this, but it it won't work across different shares, even if they're on the same host.

Long story short, your network will always be the bottleneck compared to the disk controller's native speed (~88MBps for Gigabit Ethernet vs. 200-600MBps for SATA). If you're running 100Base-T on your network instead of Gigabit, you'll be 10x slower than that (8MBps).

To (pre)view anything on the Mac, you'll always have to transfer it (or enough of it) to the Mac over the network.  For large items, I'd recommend using the Synology's interface to move or copy items between the different shares.