What is the best available performacne, assuming I can support some increase in current consumption?

For less than 2µA, over a supply range of 1.1 to 3.6V, the ADXL367 provides up to 400SPS and at noise levels that are 300x lower than the force of gravity (3.1 mg). 

For less than 2µA, over a supply range of 1.1 to 3.6V, the ADXL367 provides up to 400SPS and at noise levels that are 300x lower than the force of gravity (3.1 mg).