More information:

Since the chip seemed to get warm when I connected 3.3v, I looked at the Betz schematic, and what the schematic says it expects on that pin is actually 2.5v despite the "3v3" on the pin name. I was wondering if 3 volts was a hair too much and what I should really be trying is 2.5 volts there.

So I thought, hey, I've got 5 volts here, I can just do another 50% voltage divider to get 2.5 volts. So a couple of 10k resistors and now I had what I thought should be 2.5 volts heading into that 3v3 pin.

But that's not what I measure there. With everything hooked up, I'm getting about 60-70mv on that pin if the switch is in the down/right position, and the LED blinks steadily and the unit won't wake up. And with the switch in the up/left position, I get a varying amount in the range of 100-170mv on that pin, and the LED is dark and the unit won't wake up.

Hmph.