from my jar of silly ideas:
how about a water manometer? You are only interested in this as an alarm, right? Put colored water in a clear tube and do it optically, or slightly salty water and two wires. Hmm, evaporation might be a problem, you'll probably have to replace the water several times per filter replacement. Oil might work (lower density => greater displacement).
How about a position indicator? As the filter collects dust, it will start to deform toward the fan (it also gets more effective as a filter) and you could put a wire on it that initially has insulation against a contact, but as the filter deforms the wire would be pulled up to make contact with bare wire where the insulation stops, and you could use that for an input. Basically turn your filter into the diaphragm of a pressure transducer.
Fan speed would be another indicator: as the fan clogs, the pressure drop goes up and the flow goes down (deltaP x d(V)/dt vs. constant power from motor, to first order), so the fan speed increases; google [fan performance curve]. (and I may be way off on the fan curve explanation, but the fan does run faster when inlet flow is restricted - put your hand over your desktop fan to see).
Sensitivity will be the tough nut to crack, I expect, however change should be gradual but hopefully noticeable and constant with a newish filter and then accelerate near the end.
For calibration put a piece of plastic over a new filter with a hole say 10% of the gross area of the filter.