I would check the connection inside the PL259 connectors on your coax jumpers. Just wiggle, or gently twist the coax where it enters the back of the PL259 and see if you hear any difference while doing it. I'll guess that the actual surge current wasn't through any of the radio's DC-powered circuits. The radio's chassis and case have no DC connection to the power supply. But your coax should lead away from the radio to a ground connection. This means the fault current should have been through the shield of your coax and jumpers/ wattmeter. And whatever else was in line with the antenna coax.
I suspect the surge current from the DC power supply has compromised the connection inside one or maybe more than one PL259 connector. This would explain why adding your body capacitance to the radio's case changes the noise level.
A poor ground connection through the coax connectors would be the logical explanation. A surge of excess DC current can do that.
A continuity test on each coax jumper may or may not reveal this. Swapping a suspect coax jumper for one that hasn't been exposed to surge current might settle the question if it makes this symptom go away.
We wear out coax jumpers used on the bench here as a regular thing. Repeated connection/disconnection to a half-dozen or more radios a day tends to wear out the ground connection inside the PL259. When a radio is connected to the dummy load, any increase in receiver noise that happens when a jumper is flexed indicates one that has a worn-out ground connnection inside the PL259.
Happens a lot, just from wear and tear, even if the shield braid is securely soldered to the PL259. And if the braid was just "folded over" and jammed into the plug, that surge almost certainly oxidized the surfaces where the braid makes contact with the inside of the plug's body.
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