I think at 1Khz, the capacitor could not completely charge in one cycle.
No, that's not it. You have to make the resistance higher than the impedance of the capacitor.
Something I noticed about voltage multipliers. I've never seen two equally charged capacitors reverse bias a diode. But as long as the capacitors are completely charged the diode is reverse biased.
They always conduct. No matter what.
These two circuits are different. Resistors don't clamp a voltage. The voltages halve, halve, and halve again until Vp.
The schematic shown has a gain of 10. I changed the gain to 10,000 in this circuit. I don't know how unstable that would make it. I guess I'll have to match the opamp and output transistors.