New York City Center’s Encores! series of semi-staged revivals is fulfilling the part of its mission that meticulously restores forgotten shows we don’t need to see beyond its scheduled weekend.

“Cabin in the Sky,” the 1940 rural musical fantasy, opened six years after “Porgy and Bess,” another black musical written for Broadway by white artists. Unlike the Gershwin masterwork, however, this one turns out to be a naive period piece. Despite an A-list cast, the elaborate and loving direction and adaptation by Ruben Santiago-Hudson, and viscerally original choreography by Camille A. Brown, the production can’t shake off enough dated stereotypes to revitalize history.

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This is a hokey old story by Lynn Root about a murdered rascally sinner (Michael Potts) whose fate is postponed for six months while emissaries from heaven and hell try to claim his soul. He got this reprieve because his devout wife (LaChanze) has made a deal with the Lord’s General (Norm Lewis) who sits in a white throne on one side of Anna Louizos’ handsome watercolor set, while the devil’s son (a spectacularly amusing Chuck Cooper) attempts temptations from the opposing red throne.

The music by Vernon Duke and the often clever lyrics by John Latouche are a jaunty, if hardly revelatory mix of jazz, showbiz and gospel. “Taking a Chance on Love” outlived the show to become a standard, but the two songs that bring the stage alive — “God’s Gonna Trouble the Water” and “Dry Bones” — are spirituals that thrived long before Broadway appropriated them.

Santiago-Hudson, more often known as a director of plays, applies his elegant musical ear, insisting on a light ’40s jazz attack instead of modern show-off blasting. The chorus numbers have a special textural transparency, while wonderful dancers and Brown’s choreography — bodies leaning into their knees with unexpected swivels — rise above the comic mugging to capture the era with an all new eye.

This is one of those excavated shows for which Encores! is especially useful. Jonathan Tunick has artfully re-imagined the missing orchestration, which music director Rob Berman and the large, excellent orchestra lavish with their customary tenderness and joy. You may be amused to read in Duke’s program bio that the composer, who died in 1969, was the founder and president of the Society for Forgotten Music. “Cabin in the Sky” has been remembered, which, alas, is not the same as being rediscovered.