I think I ruled out the long run of coax by doing my testing with a 5 foot section of coax directly connected to the discone.On its own, no. They do have funky radiation patterns, which may mean it's hearing things from down in your home easier than the handheld will.
Moving it around the attic was going to be my next recommendation, but sounds like you already tried that. I'm thinking that the addition of the mount to the bottom half of the discone was probably making it pick up noises from in the house easier, but I could be wrong.
You could try shutting circuit breakers off one by one and see if there is a specific breaker that feeds something that is making the noise. Then just track down what device that is. Might be something you can relocate or replace.
So, sounds like two issues:
Local noise
Lots of coaxial cable adding to loss.
I think this is an electrical interference issue. Thanks for the suggestion of turning off breakers until the noise stops. That's my next step here.