I loved the quality and details, I wish he had done some on those topics, but hopefully someone did.
I have looked in the archive of this sub, maybe I have missed it.
Thank you
For recommendations, trivia, and such, /r/history may be a better bet.
That said there is a podcast called History of Byzantium inspired by the History of Rome podcast.
The History of Philosophy podcast has covered the ancient world and is currently starting Byzantine thought. It's an engaging podcast with a long back catalogue (started around the same time as History of Rome and is still ongoing) hosted by a philosophy professor. It's more of a podcast on the evolution of philosophy (broadly construed) but I think you'll like it.
The History of Ancient Greece podcast switches between a Mike Duncan inspired narrative history (his "season 1" which leaned heavily on Herodotus) and dives into aspects of ancient greek life and culture (what he's currently covering)
Ancient Greece Declassified is a interview based history podcast centered on ancient Greece.
As icydepth noted the History of Byzantium is a very popular history podcast explicitly in the same mold. It takes a few episodes to really take off.
About a month ago someone started a narrative history podcast on "the Hellenistic Age" (starting with Alexander). I can't speak to its quality as I haven't tried it.