I love a good dark and stormy, but I've yet to try the thunderhead. Where, exactly, does one find ginger juice? Have to juice ginger, or do they sell it at Whole Foods, or high quality liquor stores? I've never come across it.
I know that cW uses a juicer. It's potent stuff, use it sparingly.
Without a centrifugal juicer, the labor involved is outrageous. Crushing the root in a handpress has been done, but I really don't recommend. Second best option might be to grate with a superfine grater (microplane, probably), then strain through cheesecloth (though the juicer I use leaves in some of the pulp, and I don't really know if it would be better with or without). Still not a walk in the park, but as thenewgreen points out, you really don't need much. I recommend no more than 1 Tbsp. per drink, but you might want to start with even less.