Is there a way to measure tire pressure without using the valve?
If you were prepared to use  Schrader valves, you could install TPS valves used in car and truck tires. Size and possibly weight might make this idea impractical, and is most likely to work with MTB tires.  I suspect that road tires would be too small. You can get external sensors that screw onto the valve, or you would need to go tubeless to use the (probably better) internal sensors (presuming you can get a sensor that would fit a bicycle rim).
With such a system, you would simply read the display and have a very accurate pressure reading.