I had previously posted: “The A.C. voltage from BE to BE should be the same as from YE to YE and perhaps about 10 to 12 VAC. The D.C. voltage from D5 to common should be the same as from D7 to common and perhaps 12 to 15 VDC.” (actually YE-YE might be a little lower)
So let’s analyze one regulator and see if the voltages you get make sense. Looking at the +/-15VDC supplies, the A.C. voltage from RE to RE should be the same as from OR to OR and perhaps about 17 to 20 VAC. The D.C. voltage from D1 to common should be the same as from D3 to common and perhaps 20 to 25 VDC.
If you make a block diagram of what just the +15VDC supply would have to have for voltages to work, what you’re getting is not right. To get +15VDC out the A.C. secondary voltage would typically be a few volts higher and 17-20VAC is a possibility. When this is rectified you will have the diode forward voltage drops for 2 diodes but the capacitor will try to charge to the peak value of the rectified A.C. so you might have 20-25VDC, depending on load. The regulator works like a variable resistor so the input has to be a few volts higher than the output to compensate for drops across the pass transistor, the current sense resistor, and for low input line voltage. To get a constant +15VDC out of the regulator you would need a few volts higher on the input for the regulator to work properly.
When you say: “new results: YELLOW: 2.2 BLUE : 2.9 RED: 4.5 ORANGE: 2.2 (all readings VAC) -that's across the secondary windings - relative to ground each is 27-30 VAC” the secondary voltages are way low as I explained, above. The 27-30VAC you measured to ground is just capacitance coupling and not really there. Put a 1K resistor between any wire to ground and that measured voltage will drop to near zero.
If there are shorted turns in the transformer it would be really overheating and/or blow a fuse. If you are now powering the transformer through the other primary (RE-BE), measure the A.C. voltage across the original primary wires (GY-BR) and you should measure about 120VAC as well.