Thanks to the Minimoog pro for confirming this insight/suspicion.
The Expression pedal input is to a VCA separate from the Output VCA connected to the corresponding ADSR. You'll have to read the manual and look at the schemo, but I surmise that there is a +5V signal normalled through the Expression input jack which is broken when a pedal jack is patched in.
You can use a stereo male plug to use a 5V velocity signal with this input. To add an Amount control, get a pot and crossfade between the 5V and the CV signal. Have a tech do this if you have any doubt about your ability here. Don't screw it up :)
From a response at muffwiggler.com/:
"The external volume input on the back of the Mini has a switching jack that disconnects a fixed voltage going to the second VCA. The schematic shows +10v applied through a 33K resistor, giving it about a 0 to +6 volt working range. So any voltage source in that range will work. My test indicated +5 volts was not quite 100% volume."
I see that the Studio Electronics MIDIMoog has a velocity feature, but it's a switch for on/off for each, VCA and VCF. I don't know if this imparts "full" velocity or not, but evidently, these good folk knew about this possibility from the beginning. Cheers to Greg and the rest at Studio Electronics!