If you read Matthew Simmon's book Twilight in the Desert or look at this presentation you may come to the conclusion that your first version was nearer the truth. Claims of increased production capacity by Saudi Aramco or others, just quoting them, need to be treated  with the greatest caution. With their biggest oil field Ghawar,  that provides two thirds of their output, in decline, they will have to run very fast just to stay still.

The curve used to approximate oil production by Hubbert is not the Gaussian but the derivative of the a sigmoid curve, a special case of the logistics curve. See here and here. There are two justifications for using it. Firstly it fits fairly well  quite a few oilfields and secondly it has some sort of theoretical backing for a very rough picture of oil production.

The growth of microbes in a limited culture medium approximates this curve. At first growth rises at a near exponential rate but, as food becomes a limiting feature, this growth slows, stops and reverses. A reasonable realistic mathematical model of this can be made that yields  the curve analytically.

The application of this to oil production is not nearly so neat. However it does encapsulate the most important point about oil production. The biggest deposits are the easiest to find and are found near the start  of exploration in any area and are exploited  early on. Smaller fields are harder to find and have a lower yield. As a result despite increasing effort and investment output peaks and falls.

Oil fields are of course much more variable than microbes and all manner of individual political, financial, geological and meteorological factors come into play so the curves will not be accurate fits to the theoretical function. However  much of the argument is between those who imagine oil production will increase for decades to come and those who  believe the peak will come in only a few years and the moderately good empirical fit to the curve to a number of fields gives some weight to those that feel the peak is near.

The closer we get to the peak, field by field and project by project assessments will illustrate the global peak with more accuracy that the traditional Hubbert's curve based on estimated ultimate recoverable reserves (URR). Such field by field analysis according to Skrebowski is now showing a peak before the end of the decade - crucially within the range of good data regarding new projects.

I guess however none of this really addresses your point about producing nations artificially producing below their maximum.  We could avoid that complication by assuming that all producers are producing at their maximums - proving that might be tricky though!