Okay, I got the binDilemmaDemo working again, with a fit difference comparison. I choose many fit ranges, but only keep the fit result with the best chisq per degree of freedom.

Now, the fit difference histogram looks more or less like the shape of the
individual fit result histograms. Which actually makes sense more or less,
statistically speaking. So, if the error reported by the individual fit is
that width, then there may be no dilemma after all.

Thus, I had better hope that debinning can perform better than that width.