You don’t need a diff-amp if you can sample both signals fast enough. But I’d suggest just clamping one to +V and sampling the switched signal, gets rid of the offset once you subtract cell voltage. It might be good enough. Of course sampled in-between regular operation, that’s why I suggested it could be done in a blink, in-between normal operation.
Just a mad idea though.
Edit: If this is doing without the voltage divider to measure Vbatt, as I suspect, then it could be a bit approximate, but measured Vbatt vs. LED Vf should still track if they are coming through the same pin to the same ADC.
One way to make that happen, put a large pullup fromVbatt onto the ADC pin. Measure Vbatt with everything else turned off (7135 and FET). Then pulse the LED with one 7135 for a few milliseconds, if necessary turning up the gain, measure, subtract, calculate, job done. All through one pin (possibly multiplexed with something else).
For best precision, take a slightly different two measurements, not Vbatt open circuit but Vbatt whilst driving the pulse (two pulses required)…