So, I was wrong about the parts of the Trans-Labrador Highway that were finished.
Here's the situation, as best I can determine:
Phase I, from the Quebec-Labrador border to Goose Bay, NL, is finished:
Phase II, from Cartwright, NL to Blanc-Sablon, QC, is also done:
Phase III, from Goose Bay, NL to Cartwright, NL, is under construction. The Government of Newfoundland and Labrador's own website contradicts itself as to when it will be open.
(Lots of environmental impact info:
In the meantime, the ferry will take you from Goose Bay to Cartwright.
Google Maps remains a bit confused about that ferry, which according to the ferry website does actually stop in Cartwright on its way to Lewisporte.
A couple of good sites on driving the TLH:
More links: http://www.tlhwy.com/travel/links.html
A picture of the start of Phase III.
P. S. totient, I think I lack a current email address for you.