Sorry for the threadspam. Really.
Discovered something cool that might or not be a well-known thing. Alexa appears to have no trouble navigating backwards and forwards chronologically through a podcast series, episode by episode. The TuneIn API appears to provide podcast post date metadata that is easy enough for Alexa to use. And you don't have to mess around with signing up for TuneIn or anything -- it just works.
The catch? To change from the most recent episode (default when you say, Alexa, play [PODCAST NAME] from TuneIn to the next-most-recent episode, you have to tell Alexa, Alexa, next track or Alexa, next song.
So, if the Qt3 Games & Movies podcasts get added to TuneIn, we can say, Alexa, play "Quarter to Three" from TuneIn and work our way backwards through the archives. Hopefully Alexa can parse those words in the podcast title correctly.
Edit: +link to other thread