Why is the fall time of your supplies load dependent?
A high voltage power supply's output section is capacitive by design. This output capacitance gets charged up to the operating voltage. When the supply is placed in HV OFF or standby (or turned off entirely) this charged output capacitance needs to be discharged for the output voltage to return back to zero.
Most high voltage output sections use diodes in their output rectification or multiplication circuitry. The diodes are orientated to provide the required output polarity. A diode only allows current to flow one way. In a positive supply, current can only flow out of the supply. Because the supply can't sink current, the charged output capacitance needs to be bled off into the customer's load or some other discharge path.
Our positive supplies actually do have a small amount of "current sink" capability provided by the resistance of the voltage feedback divider string, located inside the supply. An extremely high value of resistance is necessary(typically tens or hundreds of meg-ohms, or even gig-ohms) so the output capacitance will bleed off to zero volts, in seconds or tens of seconds in a "no load" condition. For this reason, the fall time of our supplies are load dependent.