Summary: in order to calibrate the F1 LVDT, we need to mount an additional sensor in the suspension. Today I identified a good place to mount it.
The sensor is the LK-H022K manufactured by Keyence. The principle of operation is a laser diode emiting light onto the target surface and a photo sensor measuring its reflection. We can mount it above the Bottom Filter in order to measure the displacement of the cap. The first picture shows the -Y side of the BF, which is accesible. The blue arrow indicates where a support arm can be anchored to a nearby pillar of the security structure, and the red arrow indicates the surface upon which the sensor would measure.
I put the sensor head in the chest of drawers next to SR2 chamber.