Hi Skibber Bent.
Welcome to the LaserBoy Forum!
I think you will find that your idea will get you very close to zero volts on all channels, but there will be some differences, probably due the the tolerances of the resisters in line with the DAC channels on the sound device.
If you go with the idea of using a variable negative voltage regulator, you can probably get away with not using the trimmers on each channel input to the op-amps.
Let me know what you come up with and how well it works.
Also, remember I sell a really nice kit of the correction amp!
James.