The 8566B is not a standard Beast.
The power supply voltages are specified to a much higher accuracy than most instruments you would encounter, and for a reason.
For example, the +22V rail is specified for +-20mV, and the 20V rail for +-1mV.
First, make sure you use a very accurate DMM (the manual calls for using an HP3456A 6.5 digits DMM).
Second, your +22V rail is completely out of spec.
Obviously, adjusting the supplies is only the first step, and it will change the calibration of the instrument which is not an easy thing to correct, and requires equipment that you may or may not have.
I am not an expert on the YTO unlock problem, but I do know that everything has to be just right to make the YTO happy. You will not get far unless all rails are within specs!