Your logic is sound, kinda.
If you wereusing the lower half of the circuit to power one piece of kit then that might well work fine.
Same goes for the upper half of your schem, that would probably work fine on its own.
However I see a potenitial issue, if the mixer is connected to whatever is powered by the lower half of your circuit, then the mixers ground connection would connect to the -10v rail from the lower sections circuit, shorting out the -10v rail through the audio connections.
If you have access to 2 x 20v supplies that might work, and keep them seperate from each other, or another bit of a kludge way is to use isolation transformers on one of the items, you can get them that fit inline with the audio connections.
Dc to Dc converters are handy, however for this application noise and ground loops might be a problem, seperate supplies is the best way if you can do it.