Ham, welcome. The fact that the radio interference remained when you turned down the TV volume would indicate that the interference wasn't just riding in on a cable or power cord and being amplified along with the TV sound. That's why the RadioShack RF filters had no effect. Presumably, if you disconnect the cable TV or other input to the TV, the radio interference can still be heard? The interference would appear to be directly affecting the audio section of the TV internally at a point downstream from the volume control.
TV sets are supposed to be adequately shielded against most RF interference. Whether 400 feet is just too tough a problem, or the station is violating FCC interference regulations(have you talked to them?)is unclear. If the TV set is just inadequately protected(have you attempted to talk to the manufacturer about the problem?)there's not much that can be done as a practical matter. Aluminum foil can serve as a shield against RF interference, and you might experiment with covering various spots on the set, but this doesn't have a very high probability of success.
Enjoy the music, not the equipment.