I somehow messed up a h.264 stream's properties => stuttering

[Selur]

Now, how is this supposed to be played, or at least re-encoded?

You don't want any duplicates and thus end up with 23,976 frames.

One sure way to fix this is to resample the video to play at the original 24/1.001 FPS.

That would be the idea, problem is just to find a good method to automatically remove the duplicates and end up with 23.976 fps

In any case, it is clear the TV station changed (one time only - you can see 7x13 was broadcasted the next day) the way they speed up the show for broadcast.

I do not think so, seems more like either you changed the way you captured/saved the content or how they broadcasted it.
Both files have are created through a norm conversion.

Is there any other way, preferably done during decoding & playback?

In theory, a player could do some ivtc like thing (fieldmatch + decimate using some proper detection or pattern), but I do not know of a player that would do that.

Cu Selur