If you are not using one, I suggest installing a backup compression product, like Litespeed or Redgate backup, to make the files smalller. Or as an alternative, use a compression product (zip, rar, etc.) to compress the full backup as smalll as possible.

Also, make the full backup output multiple files, 5 or more, so that you can copy them over the network in parallel. That seems to do a better job of keeping the pipe full than copying one big file.