Finally found the gas leak in the basement--or rather, right outside. It's almost undetectable, but diffusing through the wall. Guessing there must be a break in the buried pipe and that's permeating through the soil and back into the house.
Multiple testing crews missed it--doesn't show up in the air or any of the fittings! But every few months I'd go down there and get a whiff of something so faint I couldn't tell if it was gas, something decaying, or I was imagining it.

@aphyr It's good that you found something.

Here, the gas network operator comes by at regular intervals and checks the pipes.

@bearleathermen Yeah, they do that here too, but because the leak is outside, all the previous crews missed it. You gotta get the sensor right up to a specific section of the wall and wait for it to tick up from 0.0% to 0.1%.