A follow up on this:
I ended up using the initial culture like a sour mash and tossed it in at the beginning of the boil with a 40% wheat malt/60% barley wort. I fermented it and tasted it when I bottled -- it was still slightly goaty. I tasted it this weekend, prepared for carbinated goat juice and ready to dump the 1 gallon batch. The first one actually had an interesting sweetness to it. No goat flavor. It was good. I tried a second one that apparently didn't get capped well because it wasn't carbed. It tasted goaty. I'm glad the beer ended up turning out well, aside from the carbination issues. No idea why carbination makes goaty turn sweet, but I'm glad it did.