Best way to increase attenuation in sour wort

I’ve been experimenting with pre-souring the wort when a clean lactic sourness is desired. I’m very happy with the results in small beers, like a Berliner Weiss. The issue I’ve run into is that the attenuation is very low, like 50-55%. Any ideas for increasing attenuation in low pH (2.3-2.6-ish) environments? I’ve tried rousing, but that didn’t help much. I’ve been mashing at 148-149* and pitching about 1.5m/ml/*P.

Wow, that’s a really low pH.  I only have experience with 3.0 pH Berliner Weisses.  I think just time is all it takes, like months.  How long has it been fermenting?

I don’t have any batches going right now, but gravity was stable after about a week of fermentation. The process I use is a quick and easy way to make sour beers. This process involves doing all of the souring before pitching the yeast, with lacto quickly, not relying on a long slow sour fermentation, so fermentation time should be the same as for any “normal” beer.

I’ve thought about fermenting like half the batch without souring, then blending to get the attenuation up, but that wouldn’t work for the very sour beers.