Apparently I once again need a new app that will actually download podcast episodes and keep them until I listen to them, and will consistently track whether I have listened and how far I got if I stop in the middle. Half the point is to be able to listen when I have no Internet on my phone.
AntennaPod is what I've been using without issue — fully free. Fits your criteria AFAIK, only exception I can think of is that it is based on your phone since you aren't making any account for it to track stuff online, so it'd forget if you changed phones. (Tho some data can be backed up manually.)
Only got as far as putting in rss links (which was unnecessarily difficult because old app didn't have a way to copy them out) but this *feels* like what I've been wanting for years. Thanks again.
Thanks, will look. I only use my phone. Sonnet, which I'm currently using, has started intermittently losing my place if I pause mid-episode for several days. Or if it just feels like it.
I am trying to post this but of course it was prompted by in-flight wifi not working and not being able to listen to any of the podcasts I downloaded last week, so it also won't post for a while.
Insult to injury: the display in the seat back advertising that I could use the free wi-fi to be entertained while it's not working.