terminology
OverDischarge Protection tends to be below 3v, and is impacted by drain rate.
IF you are able to read the voltage of the battery after it refuses to turn on the High Mode, then I would say its a Low Battery Voltage issue.
When a protected battery trips, it reads 0 voltage, until it gets put on a charger.
What you describe sounds like a battery that is below the necessary voltage to operate on High Mode, and the light is stepping down because of Low Voltage Step Down Warning (LVSDW), not OverDischargeProtection (ODP)
I could be wrong, but I hope you understand the distinction Im making regarding ODP going to Zero volts.
LVSDW will allow the battery to rest and work again, briefly, on a lower level, although it still really needs to be charged.
I do wish more of my Olights had battery monitors, but what works somewhat, is that the light will refuse to hold High Mode, when the battery goes below 3.4v. You report refusal to operate on high mode at 3.36v, that is a match to what Im calling LVSDW, and is not true ODP.
fwiw, the battery monitor on the Olight S1 Mini, turns on the red led on the power button, below 3.4v… coincidentally a match to your Step Down experience. Basically a 3.4v battery, cannot sustain Turbo modes.
alphabet soup!