I've tried carrot wine twice, once in a five gallon carboy and again when I got me some rain barrels for fermenting in, because carrots and sugar were the cheapest way I could come up with to fill a barrel. The five gallon barrels came out great, cleared up a lot like yours is looking, and it finished of fairly sweet. It didn't taste very carroty, but it kind of got a sort of cinnamon flavor. That stuff is all gone now, but it would've been great to mull, and the ginger is a great idea.
My barrel hasn't turned out so well, several months later and it's still cloudy and a bit sour. After reading this, I think it must've been contaminated, but I've also read that carrots actually have a lot of pectin in them for vegetables, and that all root vegetables should be boiled before fermenting. Got some pectic enzyme in there working on it right now, we'll see if that works. Did you add pectic enzyme or boil this or anything, or just the basic stuff?