I modestly propose force transducers on the radome mounts. The forces from the transducers could be algebraically summed to produce a net force which could then be processed against radome drag coefficient to produce airspeed.
That's not an altogether stupid idea. The only problem is changes in apparent drag due to accumulated ice or water striking the surface in rain.
Back in my micrometeorolgy days I'd considered and discarded this approach when looking at low cost wind speed and direction sensors.
But 10/10 in the lateral thinking stakes!