I think what I would do, assuming that Jdblse's assumption that it is a common ground issue is correct, would be to get a wiring diagram of the car for the Advancetrac, then install a new ground wire for it. This would likely mean altering one ground wire only. If you don't want to risk messing with the Advancetrac system, relocate the ground wire for each active component in the sound system.
I'm glad you posted this though, because I've had an intermittent tone come on with no message center notation and I've wondered what it is. Now that I know, I can ignore it.
Oh, and if you do this and it fixes it, you can call your engineer buddies over at Lincoln and ask them what kind of cut rate dope they were smoking when they designed that POS system.