So it turns out...
I'm incredibly picky when it comes to my podcast apps. This week I got a new phone, an iPhone, and tragically the podcast app I've been using doesn't exist within the Applesphere. Android Only. So I went shopping. Now, first just let me say: I hate paying for apps. I know, that's a pretty Android User thing to say, but it is the truth. And some apps within Apple cost $20! Or More! It is completely insane, and I don't understand it in the slightest. So when my buddy suggested and app that "only" costs $3.99, I just laughed and went hunting.
First up I looked at Stitcher. I've heard really good things about it, and I must say it is SHINY. If you don't care about bells and whistles and just want the most recent episodes of a few shows along with a Netflixian recommendation algorithm, Stitcher is the way to go. It is pretty impressive. But... the settings suck. Just to be clear, they are absolutely horrendous. Your choices are basically to subscribe or not, and what speed to play at.
I looked at a couple of other free apps, and none of them allowed me the flexibility I was looking for: to select play order, to build queues, to allow me to mark old episodes as already listened to, and to automatically delete played episodes. That's not too much to ask, is it?
Finally I found one, but even it has several downsides. First off, it uses RSS feeds instead of pulling from Apple's store, so the selection of episodes within a single show vary somewhat (as some shows retire episodes faster or slower for RSS than they do within Apple). Some shows are just plain unavailable via RSS (this was a problem when I first switched to using one that sourced from Apple in the first place, so it goes both ways). And finally...
On all my podcast posts in the past, I've been putting some statistics about what my listening time is and stuff... but I'm going to have to change the format slightly, as the information given to me is different.
Overall though? It does the trick.
Now I just have to finish importing all 100+ feeds, update the episodes I've listened to, and start building myself a playlist.