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tl;dr: 10-15 Hz.

In case you were looking for a number.

I wonder if existing weather stations might be able to pull this from their existing barometric sensors, with nothing more than software.

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It probably depends on the weather station. The cycle time on those pressure sensors can be ridiculously high and still give decent results; you really only need one measurement per minute. But that should be just one firmware patch away from being a solved problem.

I suppose the question becomes: Does 10-15Hz effectively transmit into buildings? Could the weather station base-unit, which is always powered, pick this up? Because that's where most barometric pressure sensors are; there hasn't been a reason to put them in the outdoor sensor suites which are power-constrained and harder to flash new firmware onto.

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