Running helps a lot. There are a lot of folks that won't look at non running cars no matter what the price.
I would market 2 ways. Run a continuous loop craigs list ad with at least 10 high resolution photos and 2 paragraphs. Some potential buyers know vaguely of KF, but you adding some detail about why the 51 Frazer Vagabond is important, will help motivate fencer sitters. Start high, not $6000 high. And drop every week or so.
2. Do an ebay auction. I have seen some pretty high bid counts on KF cars lately. See what the market is doing. ebay auctions- there are people set up to do KF or Hudson searches only. So it will cross their laptop quicker on ebay then craigs list