In summary, I think that the premature discoveries of super-giants can cause odd production profiles. So it would be better to factor them out before you do modeling.

No, you should never throw any data away. That is one of the golden rules of the scientific method.  Yes, I know some statisticians like to throw away outliers, but you really should do this only if you understand what the fundamentals are behind the behavior. In reality, what you want to factor out should be part of the underlying model. I might be misunderstanding you, but why not keep the "premature discoveries" in the model?

Take a look at the discovery curves published by Laherrere.

You can see the bimodal components right there. The problem is that the two modes are highly asymmetric in the discovery profile but not so much in the production profile. My own analysis leads me to believe that the second peak gets strongly accentuated by a strong increase in the extraction rate.

I have never believed in the conventional symmetric Hubbert curves, preferring instead to treat the system as a N-order  temporal response to the initial discover stimulus curves.
Ever since about 1995, the extraction rates have progressively climbed so they could keep up with the diminishing returns from the remaining amount.

The full analysis is here