In cases like this where you have a heat sensitive work piece , high wattage and high thermal mass work the best, the goal is to have the joint melted and done before the heat has any chance of flowing up the pin and heating the electrolyte, compared to the pins the capacitor has a high thermal mass, so if the time is short, only a tiny amount of heat reaches the electrolyte.
The fact that your cranking your iron so high would imply your not even adding lead solder to the joints first, which creates a lower melting point and weaker joint that is easier to seperate. After part removal you would then clean the mixture off the pads and use your solder of choice.