Is the data compressed on the remote server (thus minimizing traffic on the wire), or locally? (I'd test this myself, but the company has really strict firewall rules in place.)
The compression is done locally. If your network is slower than compression, then you could tunnel it through an SSH connection with compression enabled.
As for your parallel dump, you cannot do that to stdout and "c" format. You have to tell pg_dump the directory name to write, as that is the only format that supports parallel dumps.
