A delayed follow-up.. the gauge actually came several days sooner than scheduled. Put it in, no improvement. Continued the routine of warming up the sensor before starting the car. Today I decided to pull the gauge out and test it on the bench (using the harness and sensor that came with the replacement).

First thing I noticed is that the gauge pulls significant current spikes while it's booting up (resetting the air-core meter pointer, most likely).
Then it turns on the sensor heater via a PWM circuit, and gradually draws more and more current, up to 1.5 amps (average) @ 13.5 volts to the harness, until it gets a reading and the needle swings to the 18 AFR peg as expected. Then it drops the heater current back down to about 1 amp average.

I could simulate the drop in cranking voltage (to around 10.5-11 volts) and was able to get the gauge to stay in warmup mode (as it does in the car) even after turning the power supply back up to 13+.

At this point I gave up and put a toggle switch on the dash, in the hole recently vacated by my choke pull. Interestingly, after starting the car and then powering up the gauge (as one Autometer tech support guy actually recommended) it takes longer for the sensor to work than if I just turn the key and wait. At least from a cold start. I think the initial temp of the exhaust gas stream at the bung in the header reducer must be cooler than the desired temp, until the short time for the header to warm up

Bottom line is, it's a crappy (probably offshore) design. Anything automotive should not be confused (indefinitely) by a momentary drop in voltage while cranking. It's also exacerbated by the penny-pinching wiring harness provided, with tiny 22 gauge power and ground wires (0.016 ohms per foot each). At 1.5 amps heater current, that just adds more drop. Anyway I won't buy this gauge again... but it matches my other Sport-Comp gauges so I'm stuck with it