mm43:
To my mind the positive pressure rise on one side will be matched by the negative pressure on the other side
I don't see where this assumption is based. The idea of using the pressure drop behind an obstruction, as opposed to the pressure increase in front of it, may have some merit though.
If the device is blow-through and based on the bernoulli equation an immediate comment is that the bernoulli equation is valid only for incompressible flow i.e ~< 0.3M.
If the device is not blow-through, then the front part is essentially a very crude pitot tube, with all associated issues the engineers that have been developing the pitot tubes the last 2-300 years have faced still unresolved.