I'm afraid I don't understand the diagram or the explanation. If there is a resistor in parallel with the cap, how much of the resistance is the resistor and how much is the ESR of the cap? You don't appear to address that. It appears to me you assume that there is no resistance in parallel with the cap.
If there is a diode and resistor in parallel with the cap, how are you going to keep the diode from affecting the result with a 10 V input?
It certainly seems to me that it is critical to not to forward bias the diode so that it conducts.
I've got a few dozen caps to check. That is what makes the EDS-88A so attractive. The caps are packed in so tight that lifting one leg is not possible and getting them back in would be a huge ordeal.
Please draw out a circuit consisting of a diode, resistor, inductor and capacitor in parallel and explain how you would separate the effects of the cap from the other 3 devices with a connection across the cap. That's the general in circuit test problem.