Unbalanced isn't really the way you want to go in my opinion bud, thing is the probability factor is the closer you are to ground the more chance you have of getting noise by the sound of it.
If the cobweb is quiet it's because it's up in the air meaning that's where your next project needs to be, I made a folded diopole multiband and it was free of most noise.
Get a transistor type radio and see if you can pinpoint the noise? That would then allow you to move away from it etc.
My next door neighbour has a plasma and no matter where I site antennae I can not avoid it
You could try one of the giszmo cancelling devices but they are a small fortune and you are probably better asking around to see if you could borrow one, that would be my last resort though.
Don't you have a club with more knowledgeable members to help ? Or local chappies to help you along ?
Also please put your location on through the profile settings, and a name would be nice