[fenbach]

well, keefer,
let's hope someone else can explain why touching the controls with a screwdriver changes the sound. at least, touching the volume control. the tone control connects the plate of the output tube to ground when set for bass. i can imagine your screwdriver changes the capacitance when touching the tone control. that said, these car radios are pretty "touchy" in my experience.
you must be kidding about frying the aurora vibrator. unless you mean literally, like setting it on a hot soldering iron.
i have to think the metal covering [a mesh?] on the power wire is just a shield. a coax cable, in effect. connect both ends of the shield to ground. all the sparking in the ignition system in old cars created considerable interference.
you mentioned changing the filter cap. you do mean caps? no. 64. make sure you also replaced all the caps larger than 0.01 uf that are connected to ground. the tiny bakelite ones typically don't go bad.
are you up to aligning the radio? adjusting the various padders, that is. those adjustments will likely affect the hum. i've also found that flourescent and LED lights will introduce interference. even an AC powered power supply. not a battery, tho.