The Robert Parker record has undoubtedly always been a big favourite of Jamaican music fans over the years but I think that's more to do with overall feel than with it having a reggae or ska influenced beat (I suppose that's a whole chicken and egg debate as many of the Jamaican musicians were trying to make New Orleans R&B and it tipped over into what became mento and ska).
There are literally dozens of mid-tempo New Orleans discs with the same feel: a couple of brilliant ones that instantly spring to mind are Allen Toussaint's Poor Boy Got To Move on Alon and Willie Tee's My Heart Remembers (Nola and, if you're lucky, Cinderella).
Regarding the Cody Black 45, there's a definite syncopation which is different to mainstream American R&B of the time which marks it out as being slightly different to the norm. If anything this is even more pronounced on the other side, Keep On Keeping On, which I've always preferred to "Slowly Molding" and which definitely deserves spins in some kind of club environment, even if you can't dance to it in a typical 'Northern' fashion.