Why do you need the sallen key? For all the AC signal coming from a battery?
If you want to lower the voltage, you can use a difference amplifier. Make a reference voltage, make 12V from this, and connect it to the negative input, and indeed, your resolution will be 3-4 times higher. If you properly
Or take a 5V reference, divide your input by 2,4 and adjust your gain for full scale (again, a difference amplifier). If the difference amplifier is properly protected, you dont need higher supply voltage than the battery.
Also, be aware, that batteries have the inherent capability to power your circuit even when it is off.