A push-pull knob is just a switch cleverly hidden in the shape of a knob. It won't act as both a volume and a tone, and *couldn't*, for logical reasons. That's the answer you need.
What you really want, to have the appearance of 2 knobs, is a "cocentric" knob, which is 2 stacked knobs occupying roughly the same physical space. You could use the diagram you showed, since a dual cocentric pot is still literally 2 separate potentiometers, for 3 in total-- like the diagram.
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But, it's prompting me to think a bit outside of the box. Off to dreamland we go:
Imagine, a knob like some of us have on car stereos, in which there is "friction" when in the "down" position for adjusting the pot. The range wouldn't have to be infinitely rotatable-- it'd still have a set range that you could feel by turning all the way down or up. But when you lift, it engages an independent shaft and releases the "volume" shaft. Turn the knob to set the tone you want. Press down again to change volume. In such a knob, it'd actually be the SHAFT that determines the position of the wiper for each independent potentiometer. The knob itself would just engage one shaft or the other. So, the shafts would be cocentric, but the up/down position of the knob would allow you to adjust one or the other.
Not so sure it's an improvement over dual-cocentric, but I'm just thinking aloud...
Greg