Well, it seems like the problem is Chrome not liking AAC files (.m4a enhanced podcasts) through an HTML5 player. Other browsers work find and Chrome is fine with MP3.
This is a bit of a bugger, as I like the enhanced format for several reasons. Both from listening and procuring them.
There is a newer player out, so I will look into that. But otherwise I shall be deciding whether to go back to mp3 or to leave the podcast’s primary website only part-usable in one of the major browsers.