I like the idea.

'Nulling' the existing pressure can be done easily via the electronics. I think that with a well designed AC coupled input stage you will only 'see' the actual pulses (from the nozzle tapping the bed) and filter out any other (relatively constant) 'background' pressure (the DC and low-frequency part). With proper tuning to the dynamics of the tapping, you can potentially filter out a lot of background noise and vibrations.