This is how the podcasts look if we embed their code as we do with Libsyn.
Although the orange can't be changed these look SO much better than the Libsyn one's, and we can add as many as we want. The only slight downside I can see is that you have to click on 'DESCRIPTION' to see the details, but considering how much better this looks and that I only had to embed the link to add this podcast (instead of adding in the Title, date, description, etc, I think this is a good option.
P.S. I wrote the above before I realized that the Podcast App was more viable than I thought. This option is still available, but I don't think we'll need it.