I wound up creating a pad out of layers of duct tape. See below:
It's untidy, but it gets the magnets very, very close to the sensor, and I have completely reliable operation.
I do carry a JO counter as backup in case the battery goes dead, but I have noticed that this usually is seen when I first pick up the bike after it has set idle for some time. I've not yet had a battery die in mid-measurement.
I believe I am slowly becoming converted.