Surely, there must be a better way to do this...
Some small research time later I discovered netcat, or nc for short. nc lets you create a pipe over a network. As its man page states, it's a TCP/IP swiss army knife.
This is how I ended up automating most of the process.
On my local machine:
nc -l -p 1979 | bunzip2 | psql database_name
On the remote machine:
pg_dump database_name | bzip2 | nc my_local_ip 1979
Voila! The database dumped its data, piped it through bzip2 then over the network, to my waiting nc process which received the data, then piped it through bunzip2 and then into psql.
Cool. Another demonstration showing that Unix is such a great environment.