And if running on battery, turning off the pullup resistor on the sensor is of critical importance (by approximately 140 uA)… Went from 177 uA average to 36 uA.
Putting it in low power mode doesn’t change the power usage much at the frequencies I’m using (maybe 6 uA), but turning off the resistor definitely does.
Should probably put that little tip in the datasheet. 
Thanks for the tip (once again!) @beegee . I knew about low power mode, but didn’t realize you could turn off the resistor (it is in the ST manual for the sensor, but it didn’t jump out at me).