I have thought of a fatal flaw with my idea to use a separate actual computer power supply as the power source, which can be summed up in the phrase "potential ground loop".
So my next question is: Do any of the professional tools supply the 3.3v for SATA drives? I have read that almost all (if not all) regular SATA hard drives do not use the 3.3v, and that only some newer 1.8" SSD drives require it. This will make a difference in how I approach this. Not needing the 3.3v will make things much easier for me. I could use a simple Molex power adapter like what comes with USB drive adapters, as that would not cause a ground loop since it is not grounded. And actually there does exist a cable that goes from Molex to SATA with 5v to 3.3v converter made to power those drives, although it lacks the 12v.