Where I grew up in the midwest, there was a 500 watt station on AM 900 about 30 miles away, directionalized toward where I lived. Their signal actually got out a good 80 miles or more, but there was that heterodyne ringing sound you mention on it, regardless of which radio I used. That station has since gone dark and replaced by a high wattage station about 50 miles away on 910. I'm not back there often enough to want to listen to it when I'm in town, so I'm not sure if it suffers from that sound, or if it was just the station on 900 that had it.
I now live a block from the transmitter for Am 630 KCIS, and get an annoyingly loud heterodyne-type noise under AM1090 at home. WHich I do listen to, but have to lower the