This story was later made as the 1962 episode The Hunt (1962) starring Arthur Hunnicutt as Hyder Simpson.
In his interview with the Archive of American Television (pt 2 of 8 on YouTube), Hamner discusses writing relatively brief dramatic pieces for The Kate Smith Hour including "The Hound of Heaven." It also became the basis for his first film television credit "The Hunt" on The Twilight Zone. Hamner said he much preferred John Carradine's portrayal on Kate Smith to Arthur Hunnicutt's in the same role on The Twilight Zone
This episode exists, perhaps due to the presence of James Dean, but not readily available.