Uh.... that's not kvass. Sorry. Just gotta say. You can make it, but I wouldn't call it a kvass. More like a caraway rye beer or something. Go ahead and use the bread, and even mash and use some malt if you must. But no hops, and no caraway, IMHO. Keep it very simple. If you wanted a lemon flavor, lemon rind would be nice and actually more traditional.
I made the real stuff myself a few months ago. With Red Star bread yeast. It was okay, but...... tasted like friggin bread yeast. I decided that next time (if there is a next time) I will certainly NOT use a bread yeast, never again, but would use an ale yeast such as hefeweizen yeast or maybe even a great bready yeast such as Wyeast 1007 Altbier yeast would work awesomely. Here's the more traditional recipe that I made, and some tasting notes: