If that integrated is connected in ANY way to your Crack setup, having it on another circuit COULD be the cause of your problem. Or it could be another piece of gear connected to the integrated. Every detail you reveal about your system makes it sound more and more sprawling. Simplify to test, then add in complexity until you re-encounter the hum.
You know that with nothing connected the Crack is fine. What about with cables plugged into the Crack but not to anything else? What about to a single source? Then add the single source to an input of your switch box, the Crack to the output, and no other ins and outs. And so on. If none of these things reveal the problem, it is most likely environmental. Try the experiments in another location, even if you can only do it temporarily. What are the sources? Do they share a common denominator (i.e. are they all DACs connected to the same computer?). We know it's a system problem, but you haven't explained what the system is.
Everything matters when evaluating these issues, including cables (type, construction (how are those solder joints looking?), routing, et cetera), power, other nearby electrical/electronic devices, and so on.