The real problem is mixing psu grounds and results can be amazing depending how your home is wired and if power plug is rotated at 180 degrees
Short story do not do it
Long story ask someone who do you trust and knows that stuff for detailed explanation
Grounded plugs (|.|) can not be "rotated 180 deg". Nor can EU plugs (-|). Nor can most standard US non-grounded plugs (! |) {narrow prong, wide prong} {Even still, the rectifier isolates + from -, adding the - to the ground. The PSU will not start otherwise, it would fault.}
+12v is +12v on the output of every PSU, ground is ground on every PSU.
Dual PSU's are common, and standard, especially in servers. If it was an "issue", you couldn't touch one PC to another, or power one device from a wall-wart, that was plugged-in to your PSU... like um... USB-hubs, external drives, network cards, high-speed modems. They do not use full isolation, they all share a common ground, and have independent voltage inputs.
But you can experiment with it
However if your home is a server room and it is wired and grounded properly there is nothing to fear of
EG, plug an old CD-Drive or Floppy-Drive or any other device into one of the standard MOLEX (four prong "oooo" cables.) For the AMT unit PSU, this would be the raspberrypi as the 5v load. For the other PSU, you will need another device. (Find a nice 5v LED-light display, and you have a cool load to light-up the cards. )
P.S. An external 12v fan, will not work, as it does not use the 5v on the molex connections, though it may have a wire on the plug, it is not actually connected to anything. (It will say 12v on the fans sticker.)
...
NOTE: Without something on the +5v load, you may only have 50-80% of that amperage on the 12v rails. Voltage will actually drop to 10.5v-11.5v once the unit starts running, on the weak rail, in a multi-rail PSU. That, or it will remain 12v, but be lower available amps then expected. Only 30a-45a per rail, in the dual-rail setup mentioned above.
That is just an example. I will know more detail about each cards individual "ideal power consumption", as my unit arrives for testing.