+1 on Paul Simon Mother and Child Reunion. This really hits the mark for me, based on how OP described his request in the first post. It isn't reggae and isn't trying to be reggae, but it is a good groove that I could see a casual music fan as perceiving to be "kind of reggae."
Edit: I stand corrected. Wasn't aware of this, from wikipedia: The song was recorded at Dynamic Sounds Studios at Torrington Bridge in Kingston, Jamaica, with Jimmy Cliff's backing group. Guitarist Huks ("Hux") Brown and bass guitarist Jackie Jackson were also long-time members of Toots & the Maytals. Cissy Houston sang background vocals on the recording. The song was recorded before writing lyrics, which was unusual for Simon. He had previously hoped to make "Why Don't You Write Me" - a song recorded with Art Garfunkel on Bridge over Troubled Water - sound like a Jamaican song, but felt it ended up sounding like a "bad imitation." Simon was instructed by the musicians on the differences among reggae, ska, and bluebeat. He felt awkward at first because he was "the only white guy there and I was American." Simon later overdubbed piano and vocals to the track back in New York.