Thank you for your continued help. I was able to get the show settings how you said (I didn't realize I was supposed to go into individual shows to see that "Settings" option). I'm not sure, but I may have largely resolved my issue.
Attempt 1: Matching cyberbiker's settings (except not deleting after playing):
The podcasts autoplay, but not in the order I want, since they aren't grouped by podcast and I want them to play in chronological order within podcasts.
Attempt 2: Turning on "group by podcast":
The podcasts are grouped by podcast, but don't autoplay.
Attempt 3: Setting to "Manual" order:
I never see the three lines, and I'm unable to drag the podcasts to order them. Also, I think given the hundreds of podcasts in my playlists and the "ghost podcasts" that appear as well, it would probably be prohibitively unwieldy for the actual "playlists" I want to do in stations.
Attempt 4: Matching cyberbiker's settings but having separate stations for each podcast:
This seems as though it largely restores the functionality I want. It has a few issues:
1) I'm not 100% it's actually doing what I want, since it sometimes seems to do weird things and I haven't tested it enough to see yet.
2) It still will require some more manual switching, since I'll have to switch stations between different podcasts. This is a bit inconvenient, since the podcasts also just randomly stop sometimes, so it will require diagnostics each time to determine whether I've finished the podcast or I need to restart it. Still, this would largely restore the functionality I want.
3) It bugs me a bit from a logical/aesthetic perspective to have a "Station" that consists entirely of all of the episodes of a particular show/podcast and no other episodes. At that point the "Station" and the "Show" appear to be identical, so it seems a little silly to create a "Station" rather than just being able to autoplay the show.