Idk I'd say that the clone theory also applies to our every waking moment, each fraction of a second we're no longer the same person, even in the same body.
I don't know if there is true continuity. As we age our memories become memories of memories. Just as we don't see the nose between our eyes I think our brains turn a stuttered disjointed consciousness into what seems like a continuous stream.
It's like walking into a room and forgetting why you walked in there.
And most certainly after sleep.