For a DC control voltage input to the H8000 series, take another look at the documentation of the Foot Pedal Jacks 1 and 2 in the manual. For each TRS jack (Tip-Ring-Sleeve), the Sleeve is ground (as you'd expect), and the Tip accepts an analog control voltage (0 to +5VDC, relative to the Sleeve). So I bet you could input your control voltages using the Tip and Sleeve. The H8000 calibration procedure should also work.
WARNING — You would need to make sure your control voltage would stay within 0 to +5VDC. You would want to confirm this firsthand with a multimeter (not just reading documentation). The multimeter would not need to be fancy or expensive — the most important thing would be to see your voltages firsthand. Be aware that you would be applying your own voltage directly into the Eventide. If this feels a little scary, that’s good — that scary feeling is just telling you to think this through. Applying voltage out of range can fry the H8000.
Of course, the H8000 series also supplies +5VDC to the TRS Ring as a convenience. This gives us the more typical way to apply a control voltage to the Tip — by using a potentiometer as a voltage divider between the Ring (source) and the and the Sleeve (ground). This is also the SAFEST way to apply a control voltage to the Tip, because it is naturally limited to the range 0 to +5VDC defined by Ring and Sleeve.
With that in mind, if your application is a modular analog synth setup with dedicated hardware knobs for tweaking in real time, then you might consider making your own dedicated hardware knobs for the H8000. Instead of using a footpedal, you can buy your own potentiometers (with linear taper, not logarithmic audio taper), and run cables back to the TRS footpedal jacks. I control my H8000FW output Post D/A Gain this way.