“That’s Just Alright” backed with “I’ll Learn To Love Again” by Little Junior Parker (Duke 326) may be even later than June 1960! I believe it is from August 1960! It’s more soul than blues, so Junior must have been moving in new directions. Duke Records advertised it in the August 29, 1960 issue of Billboard magazine. Billboard featured it in the review of new records section of the September 5, 1960 issue, where they described it: “Little Junior Parker sells this blues ditty with his usual feeling over a backing by a girl’s group and rhythm.”
Duke’s next issue from September 1960 was Bobby “Blue” Bland’s R&B hit “Cry Cry Cry.” That is the latest regular issue American 78 that I have found.