The downer of having only one Earth to work with is that you have only one Earth to work with.
Models, measurements, their comparisons to expected outcomes are all that we've got in this particular scientific department. The "experiment" is comparing your best model with what happened before and what happens next, not with running the same thing a thousand times.
As I mentioned in another post, a "model" only works within its known limits. If the Earth is getting warmer outside of the limits of the established model, your model is not valid anymore. You know the xkcd joke about extrapolation, I guess?
I remember Al Gore showing the level of CO2 increase by jumping on an elevator and saying "imagine how much this increase will bring the temperature up!". But truth is, we don't know, nobody knows how much it will increase. There is no model data for that.
Models, measurements, their comparisons to expected outcomes are all that we've got in this particular scientific department. The "experiment" is comparing your best model with what happened before and what happens next, not with running the same thing a thousand times.