Another thought: how about just the way there's a national poetry day when they read aloud little bits of poetry all the time on radio 4, have
a traditional tune day when traditional tunes (excluding Barwick fair)
get played between shows, as part of continuity announcements and the like? This could extend across local radio, plus national.

And what about instead of voting for top philosopher (Melvyn Bragg's contest) favourite invention (today show) and all those others, a trad tune popularity contest?