Possibly something like four small hydraulic pistons (or syringes) full of fluid, all linked to a single piston that has a spring return.
That would give the total of all four "sensors", so 4x the average displacement.
Then link that to either a precision linear pot, or an optical encoder via a cable and drum pulley.
Other than that you would need four separate linear (or cable/drum, or rack & pinion) position sensors or encoders, then do the maths on the result.
Or, if the top plate is on linear guides so it cannot tilt enough to throw off the reading, a single transducer linked to the plate should do.
These are some types of commercial sensors / transducers:
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This type of thing, with a suitable amplifier, could be used to measure the compression force.