Depending on how you design the cylinders, you could reverse pressure to suck back the rods. So no spring involved to draw the measurement rods away from the skin.

And having a constant air pressure means all sensors press with the same force.

There are many ways to measure the distance.

You could have markers on the rod and have a camera look at a number of rods and register movement of the markers - a single camera could handle 10 rods or more since the distance between the rods are quite short.

You could have markers on the rod and let photo transistors count pulses. Similar to a rotary encoder.

You could have the rod movement drive a wheel with a rotary encoder.

You could create an inductive or capacitive sensor measuring the distance to the rod.

You could use linear potentiometers on each rod.

You could put a IR LED on every rod and capture the position of these LED:s with image analysis. One or two better web cams might be enough.