parallax is calculated by taking 2 pictures along a paralel plane, then using the half distance of that plane to work out 2 rightangled triangles, whose points meet at object. some quick trig will tell you the distance (also you get a bonus isosoles triangle to work with by combining the 2).
the greater the distance between the cameras or pictures result in greater accuracy. to measure distances of stars, a picture is taken from 1 end of earths orbit, then 6 months later it is taken from the opposite end to get the biggest plane distance and best accuracy. For a few metres though very little distance would be required (5 - 10 cm ish).
It would also be interesting to hear some results from your sharpess study (have you made a graph of sharpness threshhold against distance ? is it linear ? etc..)
Also what distance does it start losing sharpness? is it just very close?