One thing no-one has suggested so far is whether your power supply has "remote sense" terminals (usually next to the power terminals and marked +S and -S, or similar).
If you have not come across these before, they are usually provided on high current PSUs to overcome any voltage drop in the connecting wires between the power output terminals and the load. The sense terminals allow the PSU's control amplifier to be connected by separate low-current wires so that it can measure the voltage at the point of delivery to the load. It can then adjust the regulator output to compensate for voltage drop as required.
Usually - but not always - the sense terminals are connected locally inside the PSU to their respective power terminals by 100R resistors(+O/P to +S, -O/P to -S). Although this provides a safety feature in case the user forgets, or does not make, either full remote sense connections, or shorting link connections across to the respective power terminals, many older model PSUs did not have the resistors and relied on the user to connect up correctly.
The point of all this is that unless your PSU has a definite fault, the effect you are describing of over-voltage at the output, and no load regulation is exactly the kind of result you can get if the sense circuit is not connected properly.
Worth a check?