Hey Lifetime!
I can't confirm who is singing background vocals, but I can tell you that it does seem to be a Detroit-based track because of the arrangement by Dale Warren. The producer is Herman Lewis, but I can't find enough information to pinpoint him as being Detroit-based.
Also, while Chuck's version came out in 1965, the exact same track was reused for Edwin Starr's cousin from Detroit, Willie Hatcher, when he released his B-side version of the song using the exact same track in 1967. It appears Don Davis was involved in recording Willie's version as he receives producer credit along with Herman Lewis. Dale Warren inexplicably loses his arrangement credit on that second version.
Chuck:
Willie: