Here's where I'm up to. All six large capacitors have been replaced, along with the two tantalums that I pulled, thinking they were bad based on in-circuit tests which turned out to be wrong--they were good. Made sure I had correct polarity.
The large capacitors were good except for C1412 and C1414. C1414 was the worst. It reads 0L on my Fluke 87-V for capacitance (same as shorting the probes together). My "transistor tester" shows it as 12.59 nF with 14% vloss. The C1412 still shows 399 μF (rated 360 μF), but the "tester" shows 347 nF, 6.5 Ω ESR, and 3.8% vloss.
Okay, so in replacing all these, I used Alex Cuoghi's PCB's. I wanted to make sure I hadn't created any shorts due to poor soldering (my soldering looks pretty good to me, but just being careful), so after soldering the four pins into the PCB's, I checked for continuity among the ground pins to the via where the negative of the cap goes, and from the positive pin to the positive via. All good in all cases. Then I soldered the caps in place, followed by a re-checking of appropriate continuities. Finally, I soldered the PCB pins to the A9 board, making sure each was in its appropriate location and rechecking for continuity and no shorting. Then I noticed that I had not replaced the CR1412 rectifier before installing the C1412, so had to pull that again, install the CR1412, then reinstall the C1412 cap. Again checked for appropriate continuity and lack of shorts.
Time to plug the scope in again. I had a 200W bulb in series with the plug as a current limiter. Switched on the scope, and immediately switched it off again, as the bulb lit up brightly and there were sparks at the C1412 where soldered to the board. Sounded like frying bacon, but this is not supposed to be a MIG welder! Figured I had somehow created a short with my soldering, so pulled the C1412 again. No sign of any burning, so sign of solder out of place, everything still looked and measured as expected. Even pulled the cap from the PCB with no sign of anything wrong. Shrugged my shoulders and put it back in the board. Tried again with the same result. Pulled again (I know, poor board, but it seems to be handling it all gracefully). Again, so sign of my having screwed anything up. Let it sit for a day, hoping I'd think of some reason it could be my fault that there was a short. Full disclosure, I may have dropped a screw through the hole in the middle of the bottom of the board, but I don't think so. Turned the scope every which way while shaking it and there was no rattle and nothing fell out. The only other thing I could think of was that I may have cooked the CR1412 with soldering it, but I doubt that, and it did measure as good before I put it back in.
So, I'm guessing that there is a short somewhere in one of the boards, and the fact that the C1414, which is in series with the C1412 that gets so upset when I switch on the scope, was protected from that effect by the fact that the old C1414 measures in the MΩ range, and maybe the short was what killed that capacitor in the first place.
I don't yet have a Variac, but one should arrive in the mail tomorrow or the next day. Alternatively, I have a DC power supply that is fixed current or fixed voltage with up to 10A and 30V. Not sure where to feed sub 5V into the circuit to try to find the fault. Also I tried pulling all of the power connections to other boards and turning it on, but still got a sizzle at the C1412.