A few questions.
1) how is your network setup, gigabit switch or a 100Base-T router?
2) what version of windows are you using with the file transfer?
3) have you tried to use FTP to transfer your files and if so do you get the same results?
4) are these full or incremental backups and if incremental what program are you using to do this?
Note that if you are overwriting a large number of files there can be up to a 25% overhead depending on how the copying program does this (mark file for delete, write replacement file, delete old file) and the size of the files.
1) Gigabit switch.
2) I tried on both Windows 8.1 and 7 PCs with the same results.
3) I had the same result using ftp transfer.
4) I generally use Karen's Replicator for Full Backup: all new and changed files (Replicator has worked dependably for me for more than ten years.)
I've tried copying files with Windows Explorer, Teracopy, and Fast Copy. The result is always the same.
I don't think the issue is due to overwriting files as the problem occurred on blank HDs, both after reformatting the NAS HD and also after installing a new never-used HD.
Karen's Replicator has a setting to "delete old copy before creating new" and I tired that as well.
Often I enjoy the process of solving a technical mystery, but this has gone on too long and is now just a headache.