Accurately isolate force cell
Those 2N7000 are a reasonable choice, but the specified leakage current (1 uA at room temperature) would cause the effects you observe. Do you have a way to measure if in fact the FETs are leaking that much ?

In any case, you can make the circuit insensitive to FET leakage by adding additional FETs between the drain of each FET and the opamp's non-inverting ('+') input. When you switch off each sensor (e.g. M1), turn on the corresponding new FET also. The new FETs should have drain = '+' input; source = junction of sensor and existing FETs.

This works because the opamp creates a 'virtual ground' at its '-' input. By switching the bottom node of each sensor to the '+' input, the unused sensor will have nearly zero V across it and therefore will not affect the behavior of the circuit. The leakage in the additional FETs will have a negligible effect on anything else.