Suggestions for replacement podcast app?

Apple's Podcast app is well known to be a useless disaster if you like to listen to podcasts among different devices. I have been learning this the hard way with multiple Apple senior tech support advisors giving abundant, contradictory, and ultimately (to date) useless advice.

So I'd like to replace it with a 3rd party solution, that comes as close as possible to this ideal:

Lets me listen to my subscribed podcasts on my phone, computer, or pad and when synced, lets me start listening on another device to where I left off previously

Lets me play them in an order random by podcast, but in published order within a podcast (e.g., I never hear episode 3 before episode 1, but may hear

A1 B1 C1 A2 F1 A3 (A podcast episodes in 1-2-3 order) and never A3 B1 A1 C1 A2 (A podcast in 3-1-2 disorder)

Lets me play them uninterrupted (no button clicks required) for up to 6 or 8 hours at a time, offline/in airplane mode, no suddenly discovering that despite 20 syncs, the iOS device does not have podcasts B1 downloaded and so playback stops dead, over and over and over, and I have to pull over/stop working/make hands safe to manipulate stupid device to continue playback from next podcast on list.

Lets me easily--one or two taps on large buttons of a locked screen--fast forward if I do not want to listen to a particular episosde and want to move on

And deletes all episodes after they've been played, or marked played, or fast-forwarded through (ok if it only does this after some sync step).

The app must not insist on maintaining ghost episodes that screw up my general iOS/iTunes syncing and turn my devices into bricks; or keep redownloading things I've listened to or marked played on another device (assuming they were all given a chance to sync since the episodes were played).

Does such a Podcast management paragon exist? If not, what is the closest approximation that people are using?

The one feature I absolutely must have is uninterrupted playback of a series of podcasts while utterly offline.

(Apologies for duplicate posting in iPhone and iPad, but there is no 'podcasts' forum.)