I see what you mean about the voltage drop of Schottky diodes being too high for very low voltage CMOS, but as far as switching higher voltage is concerned, don't most open drain devices have internal ESD protection diodes from the output to +V? Do you know of any devices which don't?
Bipolar open collector outputs do not include them and I think for CMOS, the protection diodes are part of the body structure of the MOSFETs so with an open drain output, the top body diode is missing. The bipolar parts were often used and specified for switching voltages higher than Vcc.
I just checked the datasheet for a CMOS open drain output and it deliberately shows no high side protection diode and there is no requirement that the output voltage be limited to below the supply voltage. They were often used to translate low voltage logic levels to higher voltage logic levels.
Rather than a common emitter/source inverter, how about common base/gate configuration? That's non-inverting and there's no Miller effect so could be faster too. The only downside is the extra voltage drop.
I actually started my post discussing this but then just kept the common emitter/source part because it is simpler to understand.
The common base level shifter works great for this and is non-inverting. If base bias is provided by a resistor to say 1.2 volts, then the base current can be controlled driving the transistor into saturation allowing an output voltage down to ground so there is no forward voltage drop. In slower applications this is better than using a diode and it can still operate pretty quickly if a fast saturated switch is used. (1) (2) It is more difficult to do with MOSFETs because of their higher gate threshold voltage but I have done it with 5 volt logic.
(1) Storage time still applies in common base mode if the transistor saturates which is what makes fast saturated switches so convenient in this application.
(2) Saturation can be prevented with a Baker clamp but now the high collector to emitter voltage makes the transistor have no advantage over using a diode. I ran across this trying to replace fast saturated switches with RF transistors that had Baker clamps.