The thing w the wire touching the lip of the jack is not really doable on both sides because one side is an XLR (if I as non-native speaker understand the meaning of 'lip' right then there is no lip :D). The humming stops if I carefully wiggle the cable and then take care not to change its position/not to wiggle it any more.

What surprises me: it really sounds like a ground loop issue, but today I tried a 100USD hum eliminator and this had just no effect.

There is no humming if I plug in a headphone into teh 8NU8R, the humming only occurs with my active speakers.