My 2003 S Type 4.2 V8 Sports has an issue with interference with the radio when I turn on the heated rear screen. Anyone know how this issue can be resolved?

 

Yes this has been reported several times on the Lincoln LS forums. Mainly AM noise.

As you know neither car has an external antenna.
The antenna is the rear defrost grid.

Ford had several suggestions. No metallic window tint. This can short out the grid.
No cell phone antenna's on the rear glass either.

This is the Ford TSB and probably won't help but it's the closest thing I can find.
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I dimly recall a TSB mentioning a Link Lead - was it for this?