Sourdough can totally be made with white flour. In fact, white flour, since the bran is processed out, is naturally much lower in phytates. It also lasts much longer without going rancid because, without the germ, it has none of the oils that oxidize. If it were me, I'd keep making my sourdough starter with the whole wheat, and use the white flour in each batch as your last addition of flour (or part of that last addition), and for dusting the counter. That way you don't have to worry much about those steps not fermenting for long to neutralize the phytates.