requirements:
I use VLC
@hi seconding @continue 's suggestion for VLC.
I just use it for my podcasts (which I batch download into one flat directory as you mention wanting to play) so I can't speak to the video aspects, but I've seen support in there. It plays when the phone is locked and remembers where you left off. And in my case, I like that I can crank playback speed since I usually listen at 2–2.5× while maintaining pitch. It also has an EQ to help make some podcasts easier to understand.