In this particular case where using a battery, it is possible to introduce approx. 200 mV offset voltage between the signal ground and the negative power supply using a simple [schottky] diode.
Without the offset voltage created by the diode, the rail-to-rail op amp will not be able to swing its output all the way down to the signal ground. However, introducing the diode, the negative power supply is now about 200 mV below the signal ground and the op amp is now able to swing its output down to signal ground potential without difficulty.
Although the signal reference ground will have some ripple (60mV in this particular case) relative to the op amp's negative power supply even with the 10uF bypass capacitor, the typical power supply rejection ratio (PSRR) of an op amp will be able to take care of this "problem". Similarly, any temperature effects introduced by the diode will be attenuated by the op amp's PSRR.
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Kalvin