Yes indeed. like I say not trying to kill it off, but like to add some practical angle :-) The naysayers would be worse, believe me :-)
I had thought about timing etc off the radar heads, but I'm not sure this would work because it's probably not possible to correlate the Mode C response to the radar interrogations?.. so you'd loose the timing reference in order to make the calculation... AFAIK Mode C doesn't have a field in its return transmission which describes the radar head it's responding to (unlike Mode S where reduction of "FRUIT" is one of the main advantages, so is more controlled by the radar head itself).
In any case the current PAW implementation uses the standard widely available DUMP1090 program to decode transponder squawks, so a "DUMP1030" would be required, including the associated algorithms etc. Not impossible, but quite an undertaking. in addition you need a lot of MIPS in the DSP to be able to discriminate very small difference in the arrival time of the received signals. Timing resolution could be a challenge, so perhaps not suitable for our low cost RPi solution.
An idea I thought of which might work is the use of multilateration, based on lots of ground based PAWs that could broadcast Mode C positions using a special format over the P3I channel. Each of these ground stations use GPS timing for triangulation of the mode C reception, they then coordinate the measurements to calculate position.. I could envisage a ground network broadcasting P3I based packets to airborne PAW systems, which could give a more reliable Mode C detection method..... It's one hell of a lot of effort though! I suppose you could take MLAT outputs from FR24 and broadcast on P3I.. only issue there is that FR24 adds too much delay, so we'd get the data too late!