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Here are plots of the fit parameters for the first line to give some indication of the degree of correlation between the two fits applied to each trial:

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Warning

In performing the Xspec fits for these data, I set enumbins=100 for gtrspgen (and set the true energy range to match the energy range I gave to gtbin). For gtbin, I set the number of logrithmically spaced bins to enumbins=10 to help guard against too few events being in each bin. For the Xspec fits I performed on the Checkout 2 data, I used enumbins=10 also for the number of true energy bins. When I do that for these data, I reproduce the 20% or so discrepancy I found in my previous analysis. Having the true energy bins as queried parameters in gtrspgen is probably not a good idea. The bounds and number of bins should be set to some nominal values and be kept as hidden parameters. It should not hurt the accuracy of the Xspec fits if the true energy bounds encompass a far wider range than the channel energy bounds given to gtbin since the finite energy dispersion will effectively truncate the true energy spectrum to the relevant energy range anyways.