You've gotten lots of great advice here. Please follow up to let us know what you figure out.
If the ICs are a big help, then you're in one of those situations where almost every improvement you make will be noticeable. If that's the case, then I'd recommend going fully balanced if your pre-amp doesn't already allow it. Think of RFI with every IC and cord selection and consider putting a conditioner in the line. These improvements will be small relative to fixing your initial problem; however, when your bathed in RFI then plugging every hole is important.
Dave
If the ICs are a big help, then you're in one of those situations where almost every improvement you make will be noticeable. If that's the case, then I'd recommend going fully balanced if your pre-amp doesn't already allow it. Think of RFI with every IC and cord selection and consider putting a conditioner in the line. These improvements will be small relative to fixing your initial problem; however, when your bathed in RFI then plugging every hole is important.
Dave