As you obviously already know, power supply voltages can read just fine until the PSU is put under realistic load and then with switching power supplies, things can get wacky. I have seen some testers around which can simulate a PC load, but they are larger console tools. I guess you must make your own. What so hard about routing the power going into the tester, back out the other side to the PC motherboard? So that the tester simply sits on the line and let the PC provide the actual load. The ones by Coolmax, Manhattan and Antec don't appear to do this and it seems simple? And it would tell you if the PSU is underrated. Granted if the PC is the issue, it might not provide a load.
you can test the molex and sata connections while the computer is running but that is all, and it only gives you the green led good lights, not the lcd display.