HUM in Signal path of Pedalboard due to Voltage supply

Good evening, everyone,

I have a rookie question, but please don't laugh at me now:

I built myself a pedalboard for my electric guitar. On it are three devices, which all need different voltages:
One needs 12 Volt, one 9 Volt and one 9 Volt but with plus and minus pole inverted.
So I bought a 12 Volt power supply. The line splitter itself on two ways on. One goes directly to the 12 Volt consumer and the other to a 12 to 9 Volt voltage regulator.
Works fine but as I told one device needs the 9 Volt inverted. So I took a y-splitter cable and on one output path turned the wires around. This also works fine but unfortunately I now have a hum in the signal when I connect both 9 Volt devices. If I disconnect the inverted one the hum is gone.
I suspect that this is a ground loop. If I hang a DI box at the output and press the ground lift switch, the hum is gone.

Therefore now finally my question:
Would you just use the DI Box and leave everything as it is or can you solve this better by inverting the 9 Volt so that there is no humming at all?
 
Look carefully at the two with the 9v at opposite polarity. What matters is which side of that is grounded inside the unit. In general you will find the negative side is grounded while the +9 is the hot for the circuits.