From my perspective there would be no sonic benefits from going balanced into the BHA-1 since, as you say, it's converted to single-ended any way. My BDA-2 sounds the same driving the BHA-1 either way. I currently own a Bifrost and formerly owned a Gungnir. My advise is to just enjoy your Bifrost. The Gungnir is a slight bit better, but the Bifrost is nearly as good. A worthwhile upgrade wound be the Yggdrasil.