But the sensor has to be able to measure a force of 250 lbs.
Are you talking about the total force applied to the patient? These are fairly small sensors and the force will be spread out over an area much larger than the sensor. Unless you design a mechanical means to transfer 100% of that force onto the sensor (less than 1/3 square inch) the actual pressure seen by the sensor will be much less.
250 pounds applied 100% to the sensor would mean a pressure of 750 Pounds per square inch.
The FSR-402 is rated for 22 pounds of force which would be ~66 psi.