The DataFrame Class will have the origin of the data frame in page units, but the location of points in the layer aren't referenced in any classes that I know of (my lack of knowledge on this is not an indication of very much).
You may have better luck by converting your points to graphics then using the arcpy.mapping GraphicElement.elementPositionX, GraphicElement.elementPositionX class (or Pro equivalent).
I would also do physical trials to see if print margins etc. are included.
I had a think about this.
You coukd get the origin coordinates of the extent of your dataframe, then take the shape x,y xoordinates of each point and minus the dataframe origin coordinate values.
the dataframe also has a scale attribute value which you can then divide by to get the paper distance(x,y) of each point from the dataframe.
then add these values to the x,y position of the dataframe.