If I didn't have a discharge function on any chargers and I felt the need to occasionally fully discharge cells, I'd probably wire something up with power diodes and resistors in series for each cell to discharge them individually.
That way the diodes would limit how far a cell could be discharged even if I left cells in it for a long time.
Not quite 'automatic cutoff', but stops them getting entirely flat.
The ~1.0V/0.9V is more critical for cells in packs, since they have a risk of being discharged to the point of polarity reversal, which isn't an issue when cells are discharged individually.
Discharge current would depend how quickly I wanted the discharge to happen - if I was content with a low rate (5h AAA, 10h AA) I could use small diodes (like 1N4001) and limited-size series resistors without being particularly concerned about anything getting warm. I'd be likely to tweak resistor values after seeing how things went (and what forward voltage my diodes typically had, but with maybe ~0.8V voltage when passing low-ish currents, and a target current of ~200mA, something in the 2R ballpark would seem about right, and would only be generating ~1/4W of resistor or diode heat with a worst-case cell voltage of ~1.5V, much less at ~1.2V.
Unless I was expecting to be discharging a lot of cells at once, or discharging them more regularly than the likely few times a year which seems suggested to keep them exercised, I'd be happy with that kind of timing - if I wanted more speed, I'd probably halve the resistance. The less intervention I needed to make, the less I'd tend to be concerned about speed.
