You tryed what, replaced the zener at the opamp output by two diodes as Jan proposed or evt by a led ?
If a divider (1k+1k) from 5V3 doesn't produce 2V65 but 2V53 there is something wrong.A resistor not 1k or a leaking diode ... Not the capacitor leaking, gives a deviation the other way.
Mona
What puzzles me is the large input voltage delta at the opamp, presumably 20mV. Those opamps don't have so large input offset.
Jan