Would you say this one works c. Not twice did I lose to him. I lost to him five times.
My feeling is that it doesn't. I would say the first sentence is more or less equivalent to I did not even lose to him twice. There is emphasis in the negation.
It seems debatable. "Not once did I lose to him. I lost to him five times" is not right (except if said for deliberate misleading effect). However, "Not twice ..." is not idiomatic like "Not once ..."; it is an unusual stylised form whose usage is not so clearly prescribed.