VCO for synth V/Octave and battery supply?
There are reasons why analog synths are largely obsolete today, and the main one is that making a good VCO that stays in tune over a wide range of voltages and temperatures is super difficult.  I suggest an alternative, hybrid approach.

Use a simple microcontroller, either with the built in DAC or external audio DAC, as your "oscillator".  The input to the MCU could be an analog voltage to the internal ADC, MIDI data, or some other digital data.  The output would be a sine wave of the correct frequency.  The output then goes to your analog circuitry of choice.

Be sure to run the MCU off of a real XTAL or quartz oscilator and not from the internal oscillator.  The internal oscillator is not accurate enough to keep things in tune.

The cool thing about this approach is that you can easily output things other than sine waves.  Square, triangle, sawtooth, or something "custom" is just as easy as a sine wave.  This gives your analog filters more harmonics to play with and create more interesting and useful sounds.  Oh, and it is fairly low power when compared to the typical ways to do VCOs.

The first "digital" synths in the 1980's used this hybrid approach and is really the main technological advancement that made synths have a wider market appeal-- at least until we have the processing power to do it entirely in the digital domain.