The good news is that 61 volt spike is gone. The bad news is that I'm still getting a fairly decent spike around 36 volts with the PS recalibrated at 30V 3A which is tp be expected given a 36V zener I suppose.
The output should never rise above the set point when power is applied or removed. I am inclined to believe that there is more than one problem but the lack of any regulation or protection on the supply to the operational amplifiers I consider a design flaw.
At this point I don't know if this is inherent to linear supplies and inrush or if the circuit just needs some rework to catch this and shunt this based on P1's setting somehow. I'm too new to this to know off the top of my head what needs done but I have a feeling that a solution might be in the PS-503 service manual schematic. I might have to build one of these just to probe around in it. Some of the parts are unknown such as some the transistors and all of the op amps. The manual doesn't say much about these other than their part designation so I looked up the part number and get back C741C so I'm assuming some sort of oldish 741 op amp.
The PS-503 design is pretty dense and unconventional in some respects even if you ignore the complexity added by being a dual output design with tracking. There are changes I would make like having the output amplifiers operate with a fixed gain and varying the output from the reference because it would make the frequency response more predictable.
The PS-503 operational amplifiers are just 36 volt 741 types and not critical. Besides qualifying their sources, Tektronix graded incoming 741s and the ones with high bias current, high offset current, high offset voltage, and high offset voltage drift are the -00 ones used in non-critical designs. They actually graded them for 40 volt operation as well instead of buying the 741/A/M version.
One of my PS-503s has a pair of 301A operational amplifiers for U55 and U155 but they and one of the 741s are in sockets so I think someone who knew what they were doing repaired it in the past. They added the compensation capacitors needed by the 301As to the back of the printed circuit board.
Either way, it's working much better than it was and even though it's still spiking, at least it's not as bad as it was. One of these days I'll manage enough money to get a real scope and perhaps help tame this thing if I haven't already. I have another meter in mind and I think that I probably need to get an analog or two just for when things like this are going on. I do appreciate your help with all of this. I'll keep updating for posterity if I figure anything out.
Some multimeters have a pretty fast peak detect mode.
Any storage oscilloscope is handy in cases like these. DSOs are particularly useful for diagnosing startup problems and even an old and low performance unit can handle something like this. I very rarely need to use anything better than a Tektronix 2230 which is the oldest DSO that I can honestly recommend.
I would never recommend a USB DSO unless it had a unique and useful feature like the ones from CircuitGear which support low frequency vector network analysis. That is particularly useful for designing high performance power supplies.