How do I condition a signal with an op-amp that needs a negative rail where one is not provided?
The accuracy of the ADC is determined by the number of bits.  A higher voltage range for the ADC would stretch the bits out reducing the resolution, or rather increasing the step voltage.
You don't need a negative voltage for the op-amps if you offset the input by Vcc/2 with a simple voltage divider. This could be in the form of a false ground reference to the input of the op-amp, as shown in this schematic:

On a 3.3V system that would off-set the input voltage by 1.65V making it from 2.06V for 0PH to 1.24V for 14PH.
Increasing R_F by a factor of 2 would increase the gain to 2:1 making it a +/- -.82V swing - 2.47V to 0.83V thus increasing your precision.
A further increase of R_F could increase your precision more, until you hit the top/bottom end of the output headroom.  A &quot;Rail-to-Rail&quot; op-amp would give you more headroom than a normal one.