OK, I did a few more experiments. I think I can conclude leakage current of caps is greatly overestimated. I think the best experiment was the one with op amp. I used LM2904 powered from 9V (single rail) in this configuration:
The bias current of the op amp is about 37 nA (using 10M resistor instead of C1 led to ~370mV at output of the op amp). I discharged 1000uF/6.3V cap. At first the voltage on the cap (measured as voltage on output of op amp) increased by about 1V/8h - which means nearly all of the bias current was used to charge the cap. Then we left for weekend. When we returned voltage was close 6V but it still grows - about 0.1V/8h. So the leakage current of the cap is still lower than 37 nA bias current but close to it. It is consistent with the fast leakage current grows when close to the rated voltage. But despite the voltage is around 6.2V now it is still less than the bias current - and that is much much less than expected leakage current (but I must admit there is hardly 20°C here - it would be surely worse @ higher temperature).