Absolutely no way its working for you
I have rebuilt that circuit ("high side" sense amplifier) several times now and it has never worked as expected. In fact i redid the circuit again, this time with different voltages (9v supply, 4 volt inputs, 10k resistors) to make sure I'm within the common mode operation of the op amp and it still didn't work (output couldn't swing below 0.6V).
Having changed everything twice over, I decided to redo the circuit again but use higher value resistors (200k vs 10k previously)
To my absolute surprise, after having changed the resistors only, the circuit is now working flawlessly now
PSR B1257, did you use 10k resistors as well?
Thank you all for the assistance!