hmmmm in terms of ideas...
- have it cut in and out?
- layer it with other 'noise' - radio static/radio dial sweeps/distoerted radio-y vocals/satellite bleeps and bloops?
- What made it especially obvious that it was a result of a noisy module/hum was that when the bass comes in it 'ducks' the noise, and it fades back in - making it clear that it's not an additional ambient layer on the composition.
As I don't do much live/dawless stuff, the solutions above are maybe more acheivable in a DAW. Not sure how'd you'd go about some of those ideas on your rack...