Since this is a battery-powered system I do not advise running the Schmitt trigger itself from an LDO. Run the trigger's comparator on Vbat itself and choose a comparator that
- has sufficient PSRR, since you expect your supply to vary;
- is rail-to-rail; and
- supports a single-ended supply at the voltages you expect.
Use a low-power reference such as a fixed, 2.5V LM4040 for your negative terminal. This draws as little as 45uA typ, though you'll want to exceed its max of 60uA in the worst case. Your threshold analysis will need to take into account the two different supply voltages expected at each threshold. In other words your hysteresis curve will not be rectangular but will look, crudely, like

with transition analysis points in red. A possible solution for this system is

simulate this circuit – Schematic created using CircuitLab
where
$$
\frac {R_2}{R_4} = \frac {69} {65} \left( \frac {13} {V_{ref}} - 1 \right)
$$
$$
\frac {R_3}{R_4} = \frac {69} {4} \left( \frac {13} {V_{ref}} - 1 \right)
$$
This yields the correct results:
