Some questions about power supply noise and transducer wiring
Your CM ground has an output impedance of 5~10 Ohms with the sensor being ~1K but load current for the MEMs accelerometer "may" be fairly constant. (verify) Otherwise Load regulation of supply may affect noise floor, if important.

CMRR depends on frequency of interference and impedance ratio of load to source for CM attenuation and balanced cable and Diff impedance help. Ferrite chokes and shunt caps will help with AM/SW interference on long cables. (AM Antenna effects).

Is there a DC offset needed for gravity?  or is this just for structural vibration?

Alternative  precision rail splitter

Supplies 20mA virtual centre V gnd to 10mA sensor

For apps needing more current using an Op Amp to drive the emitter follower pair with direct feedback and split rail RC on Vin+ works.

Dual Batteries are good for lower ESR, high surge currents but also generate more thermal noise easily filtered for analog situations.