Never mind about the T3 transformer, I managed to test it on top of another transformer, and it was OK.
Today I followed up on an idea to check the -5.2V rail which is -0.01V (voltages are listed in first post) based on the assumption there is a short somewhere, and that causes the rest of the voltages to drop to half as well.
So without mains connected, I just measured resistance at the 20 pin output power connector on the PSU, and started to see a pattern where voltage output pins had a few k ohm resistance when measured against ground except -5.2V which was a dead short. With this in mind I started to desolder everything in the trace path from that -V5.2 pin (ignoring the schematics), regulation control board, transistors, electrolytic capacitors, regulators, T3 transformer (was out already), and so on, after removing each I checked for the short between -5.2V and ground pin, and the short was there even when the whole path was pretty much empty except for a few passives. Then I noticed that one of the pads for C19 (previously replaced capacitor) on the top side of the board was a bit dark from cap leakage, so I cleaned it up with rubbing alcohol and it became visible that the pad was isolated (circle shaped border) within another broad trace, measured again and now it was ~200k ohm between -5.2V pin and ground!
After that I soldered everything back, checking resistance between -5.2V and ground just to be sure the problem wasn't back. I powered on the PSU with an incandescent flash bulb in series with mains just in case (as recommended by George), measured +5V at the external control point and the rest of the voltages were OK.
Two weeks of repair finally over, learned a lot about power supplies in the process. Thanks for the help Toasty.