Two different kinds of Tire Pressure Sensors

Last winter I bought a used set of steel wheels on which to fit snow tires for our '02 Chrysler 300M, which has a tire-pressure monitoring system that is "trained" using a large "donut" magnet on each valve stem in turn.
I wasn't bothered about the absence of tire-pressure monitors on the steel wheels, but the shop said that if the car had TPMS originally they were "required" to fit them, so I let them fit a new set, which meant that the car's TPMS system had to be programmed to recognize them -- until the system was programmed it complained about not being able to recognize the sensors. All seemed to be well after the original programming.
When I put the original wheels back after last winter, the TPMS system seemed to work fine. IOW, the car's TPMS system seemed to recognize both the new and the original sensors.
Now that I have reinstalled the wheels with the snow tires and new tire-pressure sensors, the car's TPMS system is not complaining, but the tire pressure readings are all over the place and nothing like the pressure shown by my digital tire gauge. The magnet does not work to retrain the system.
Anything I can try other than simply returning to the tire place?
Perce
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Percival P. Cassidy

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