If you applied an alternating magnetic field across the valve, parallel to the check shaft, say by means of a C- shaped armature with pole pieces near the valve seat, you might be able to measure, say with a linear output Hall effect device on one pole, a change in the valve's magnetic impedance (reluctance?) depending on whether the poppet was in the seat or not.
I'd expect a small signal, and you'll probably need to also measure the temperature so you can compensate the LOHED.
-Mike-