... If I separate the red and white wires, do I connect the white to the top of the pot as I have done with the green and bare, and connect the red to where it is now in the side hoop?
Correct. White to the top/back of the Vol 2 pot with the green & bare, and red to the loop/lug on Vol 1.
Try that and let us know the results. We'll look into the tone after that, if needed.