Well, it turns out that the professional version of Friendster that I've
been talking about/looking for already exists. Never one to re-invent the
wheel, I've signed up at
LinkedIn.
It looks like it pretty much implements all of the features I'd like to
see in a "social" network designed around people's professional lives.
They have different terminology, but most of the features I'd thought of
are already there and work. I still need to enter all of my "experience"
and build my profile, but the rest of the information should be there
soon.