I would argue that a parody is not always a negative imitation of something, nor is it always intended to mock. What it is is something that imitates another thing in order to comment on it. For example *The Wind Done Gone* is a novel that retells the story of *Gone With the Wind* from the PoV of the enslaved characters. By doing so, it comments on the original, as well as making some new points of its own. **That** is a true parody, IMO.

In any case, one does not usually speak of parodying real events. When one attempts to closely imitate the style of another work, usually with a positive intention, although not always, that may be called a "pastiche". But one does not normally pastiche real events, either.

One might speak of "fictionalizing" real events, or of "idealizing" a real situation. One might say, for example, that *The West Wing* was an idealized version of the Presidency. 

I have also herd people use the phrase "X done right".  For example The Commonwealth in Charles Stross's "Deep State" series has been called "The Soviet Union done right". This means to take the basic concept of X (whatever X might be) and write about it being implemented in a different way, so that the mistakes which happened in the real world are prevented or countered. one might speak of *The West Wing* as "The Presidency done right".

Would either of those phrases fit the meaning you intend to convey?