I have limited experience fixing these Tek scopes, but this is what I would do .... assuming that it is the 7603 Linear supply and that your comment "When I disconnect power from the vertical amp board the supplies lock in and are stable" means the values as stated above.
Check results with another Meter.
I assume that the voltages quoted are regulated voltages from Pin 971 .... my experience would indicate that any 'downstream' loading of the supplies would turn off one or all of the supplies .... not lead to a general lowering of all voltages. There small resistors at outputs of each regulated supply performing this function eg approx 1 ohm resistors ... check them.
My guess is that something 'upstream' is causing the lowering of all supplies. Check UNregulated voltages at Pin 980 ..... then secondary transforming voltages etc.
Is the voltage selector suitable for your location??
Hope this helps.