The problem with a single 10k pot in series with the group of 50k pots is that the point where they join is not 'stiff', is not a low impedance like ground. This means that adjusting any of the 50k pots will, as you've found, move that point and so alter the other oscillators.

The oscillator configuration you have chosen is also amenable (to some extent) to voltage control as well as resistance control, which allows you to have a low impedance solution.

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