I agree with Scott, no need to use rsync - he should have used rclone instead! It can be easily installed in the package manager, and with 4 threads (or multiples of 4) it fully uses/saturates the 4 1GbE links.

Also a hint for anyone planning something similar: if you use Synologys SHR format (based on mdraid+btrfs) and your new destination supports or uses BTRFS too, you can just btrfs send your whole pool to the new NAS!

(Since its a single process it wont saturate any LAG though)