AntennaPod looks nice, but I do use the Web version of Pocket Casts a lot. It wouldn't be too hard to switch back to gPodder and Rhythmbox, but I love that state syncs between the Android app and web player. It will be hard to let Pocket Casts go (if it does become a spy).
I'd really love to use AntennaPod but they're missing the key smart playlist feature I love from BeyondPod. I don't even have to open the app most days and I can easily switch to a different set of podcasts when my wife is in the car. Does AntennaPod have anything similar that I'm missing?
Additionally you won't have any new requirement to create a new account or pull analytics from your listening habits as you mentioned towards the end.