I think what I would do is just remove all cables and make a recording of the oscillator for, say, 10 seconds. Make a sample from it. Then next time, just play this sample and tune the oscillator to this sample before you starting adding voltages. Move the Coarse and Fine knobs until you don't hear beating.
If you want to be perfect, make sure that your tuning note is an "a". But this is already academic, there is no real reason, as long as it is only your oscillator that must be in tune to your samples.