I love beet kvass! I make it all the time. The trick is to let it ferment long enough, which is usually longer than Sally Fallon says in NT (where I am, at least). I never use whey anymore.
You can use salt or not, but I don't recommend using as much as she says. I use about 1 teaspoon for 1.5-2 quarts.
For starters I have used just salt, just lemon juice, salt and lemon juice, S. boulardii from a capsule, other probiotics, etc. I usually save about 1/2 cup of the fresh previous batch as starter for the new batch, but it needs to be at it's prime in order for the new batch to have the right microbial balance to ferment properly and taste good. If I let it go too long before starting a new batch I just use a different starter.
I haven't made the recipe in WF but I did make the pickled beets, and used the liquid from that as a starter beet kvass, and it turned out very well.
I usually stir it once a day while it's fermenting. It's done when it's not translucent anymore. It should be a very dark, brilliant magenta-purple. Slightly acidic and a hint of effervescence. It shouldn't taste like swamp water, or salty beet water.
I use it with meals to help digestion (HCl production/replacement). Sometimes I put a bit of ACV in it for an extra kick and to enhance the acidity.