An additional piece of information.
Remember I first said hum was on both channels and the said left channel only?
I was right both times. When connected to the tape heads I get hum on both channels. When inputs are shorted hum comes only from one channel. When not hum comes from both channels. The noise is not picked up by the heads or the wire because the Repro is silent with the same deck in the same position.
There's a very slight reduction in hum if I connect the ground post to the deck but almost insignificant.
At this time I'm almost sure I have a ground loop.