None of the versions of "Go tell it on the mountain" that I know has that repeated three times; everything I've heard or seen is more along the lines of

Go tell it on the mountain
Over the hills and everywhe-e-e-re
Go tell it on the mountain
That Jesus Christ is born

(the second line of which is metrically quite hard to accommodate to the dead goose tune; however, the "go tell" lines and the finale are indeed quite similar, and there's no reason it couldn't be sung that way. question is, was it ever?)

Liland