LM13700 Control voltage?
I've never used this device so I'm only answering half the question - the bit that relates to the gain control input. It's always worth a look in the data sheet. Here's what the equivalent circuit is: -



On pins 1 or 16 the maximum voltage can only be the Vbe of Q2 plus the diode drop of D1. This is going to be somewhere between 1V and 2V relative to the negative rail.

The resistor in series on your circuit is to attempt to convert a variable voltage to a variable current so yes, it is possible to deliver the variable constant current drive from a much lower voltage, probably from as low as 3.3 volts above the negative rail.