I've read that the "real deal" Berliners today are brewed with hardly any, or no wheat at all. I think the "Weiss" part is more indicative of the color rather than the ingredients. I've never been to Berlin, so I have no idea what they actually taste like.
I've never made a beer like what you're describing. I pre-sour my wort for three days with a sour culture made from base grains. After three days at 100-110*F, I'll boil half the wort for 30min with my hops, and I'll bring the other half of the wort up to 150* for 30min. I'll chill, then pitch onto a yeast cake. This method provides a very quick, repeatable and clean souring, with the added benefit that everything "downstream" from the BK should be bug-free.
It doesn't help you this time, but it might be worth trying in the future.