Podcast downloaded from other source not appearing in app

One of my favorite podcasts is no longer available through iTunes but can be downloaded directly from the producer's website. I've done so, synced to my iPhone with those podcasts checked off, but while the name of the podcast is showing up in the Podcast app, the actual podcasts are not. I've also tried changing their genres and media kind to see if they would show up in the Music app but nothing seems to be working.

How can I get these podcasts to appear and play correctly on my iPhone? Any suggestions? I'm using iOS 7.1.