@Chuckey Your method doesn't work because the film is not uniform; its resistance is 10 times higher along one direction than along the other. Also, with regard to the technical details you provided, I don't think I'm going to use DC. I use AC Lock-In amplifiers that can measure the signal more accurately. They also have 24 db/octave RC filter, plus I do additional DSP in computer. When they measure voltage, they provide high input impedance so external op amps should not be necessary.
EDIT: if your method is to source current along two opposite corners and measure along the other two, then this is not an Ohmic measurement, You should only source and measure along parallel pairs, not crossed ones.