I have not tried this with a Berliner Weisse, but I did do it with a Flanders red, and it worked very well. I was rereading Raj Apte's treatise on Flanders red and brown ales, and he noted in there that brett and lacto produce more souring components when they are forced to work on starches rather than dextrins.
I took about 1/2 cup of flour, and boiled it in a couple cups of water to sanitize, and then added it to the fermenter. I gave it another couple months, and now the acidity is right up there. You could also see the starch haze disappear over 1-2 months.
I also agree that a sour mash may be your best bet.