The math looks right.
They might be able to get a better estimate of the high end of the range using a balloon. Put the sensor in the balloon and squeeze the balloon down around the sensor to get all the air out. Attach it to the gas outlet and partially fill the balloon with gas then take a reading. Needless to say - NO SMOKING ]
That ought to be very close to the top end. It'll probably be quite a bit higher than 690 but they can just plug the new value into the formula to derive k and away they go.
Pete