There are some problems with the original circuit, the primary one is low gain and biasing as-if this was a current mirror, where - instead - a differential pair biasing is called for.
It also won't work at such a low voltage due to the Vgs(th) of the PMOSfet. A microcurrent oscillator and a charge pump would be needed to fully turn on the mosfet at single-cell voltages. Parts of this circuit could also be redesigned using small-signal mosfets - I'll revisit that later.
We essentially want a comparator built out from a differential pair. If such a comparator is driven from low impedance nodes, the drive voltage can be equivalently provided on the emitters or on the bases. That's what this circuit does.
simulate this circuit – Schematic created using CircuitLab
A differential pair with emitter inputs only needs a bias current on the bases. R5 takes care of it. R3 and R4 suppress positive feedback across the comparator, with R5 acting as a long tail load, "reflected" to the common base node instead of the common emitter node. That's why R5 can be pretty large: its conductance is multiplied by the current gain of the pair, acting as-if it was at the common emitter node.
R6 decreases the gain of the left leg of the differential pair when the diode is turned on.
Some compensation will be necessary if R9 is much larger (say 1k or more).
This circuit was built and performs reasonably with right side at 5V and left side between 0V and 10V.