I think you lot are being partially blinded by the look of the internals.
I certainly wouldn't call it a death trap. Much of the circuitry is low voltage and CRT LOPTs especially with separate Triplers (as opposed to diode spilt secondaries) are getting much harder to find. In addition, you have a reasonably enclosure, ready fitted meters (ok the volts one's calibration leaves something to be desired) and matching high voltage output connectors.
Yes, the construction is crap, but it is basically functional, withstands arcing of the output, and apparently works reasonably well as an EHT leakage detector so the basic circuit must be fairly sound. I've seen much worse and far more dangerous starting points for an EHT supply! I think it's worth at least putting a higher value HT rated resistor in series with the output*, partly to reduce the 'shock value' (remember the tripler has capacitance), but mainly to protect the tripler itself from overload, and characterizing it a bit more before considering whether it is worth a proper rework.
Don't forget to drill down to the mains primary side and make sure everything is well sleeved - an EHT flashover to mains can cause a nasty (hopefully constrained) high current flash events - this was occasionally a failure mode in old CRT colour TVs.
Edit: *On second look, I can't see from the diagram whether the output series resistors are 100k or 100M (in which case they should be ok).
P.S. Did you eliminate corona discharge at the end of the output cable as a source of the sound at the end of the video? Another culprit may be the un-potted resistor in the top of the tripler. My 10kV insulation tester produces plenty of noise from the end of the probe when the ground connection is that close and will trip on the bottom two current ranges without visible arcing. Get it to that same state, stand away from it and darken the room, the source should be obvious.