The diodes are there to prevent the output of the circuit from falling below 0V (half-wave rectifier). Maybe you did not try your circuit with CVs that would have required this protection.
The AC-coupling is needed here because this circuit processes audio signals referenced to ground. It is not needed in your application.
But you need the stabilization network, though (220 ohm R and 1200pF C).
Stop! You’re back playing the “voltage controlled resistor” game, where you want to replace all resistors by complex circuits without considering what they are used for.
I’ll take this simple example: you have a pot with one end hooked to ground, the other to 5V, and a voltage at the wiper sent somewhere. So the whole circuit is just a divider, used to generate a voltage varying between 0V and 5V. How to make this voltage-controllable? Do you replace the pot by a “Voltage-controlled resistor”? No, you just send your CV (optionally scaled/clipped to 0…5V) where the wiper of the pot goes.
Same story here, except that the function played by the pot you want to replace is to generate a varying current.