I'm thinking about this, so I'll mention it for you to consider.
It sounds like the AC hum is being induced into your circuit.
Are you working around a flourescent light, or some other electronically noisy device
while you're working on this? The power outlet tied to some other device that might
be inducing the AC hum onto your circuit?
I'm wondering if you're working on your circuit, and then moving to another circuit when
you're comparing the operation of what you're working on, with other fully functional
circuit.
Just something to look at, while you're working on this.
Some people on this site believe they have insight that I don't intrinsically possess,
so you may have a better suggestion from someone soon.
As a fly by the seat of my pants tech, I'd start experimenting with where your grounds
cancel the hum and where they don't.
Is the cable wire you're using for you new circuit 'shielded' (the wires have an aluminum
foil jacket or wire mesh under the insulation, around your signal wires)? That helps
to keep stray signals from being induced onto your signal wires.
I can't see the circuit, but you're already doing your own experimenting to isolate the
problem. Hopefully, you'll find the solution easily soon.