Yes, sounds as if the 5V supply can't supply enough current to get more than 2 of them started up. There may be an inrush current surge at turn-on that is upsetting the PSU. As you say, feeding 12V into pin 7 is an alternative. It may also be safer if there's an internal regulator in each of the drives to drop it to 5V by the sounds of it. Pretty sure that's what I did for my 3 drives.