Buster Brown was the artist on one of the most famous late 78s: “Fannie Mae.” In April 1960 his “The Madison Shuffle” b/w “John Henry (The Steel Driving Man)” was issued as Fire 1020. Billboard’s “Reviews Of This Week’s Singles” from April 25, 1960 describes this record as, “Brown could click again via either one of these powerful sides. ‘John Henry,’ the old folk song gets a shoutin’ approach over a rhythmic and danceable ork setting. ‘The Madison Shuffle’ is an instrumental side that features harmonica over a snappy ork assist. Both are dual-market sides.”
“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.