63 Dart Radio issue

The audio amplifier can become unstable and oscillate if voltage dips under 8, or 9V or so. A brief interruption in voltage to the amplifier can also make it take off and sing.
May be driving around is aggravating a loose connection in the feed or ground?
Since the radio has been serviced I'm certain all capacitors are fresh, but a hairline crack in the printed circuit board could also be a cause. See if you can rap the radio chassis with a screwdriver handle and make it act up. Sorry I can't be of more help. Keep us updated on your findings.