You are fitting the sum of two functions that only differ slightly in their shape, and your data has no sharp or distinguishing features that forces the fit to a well defined, unique, solution. Based on considerable experience, your fit is probably ill conditioned, and the estimated errors in your parameters are not reliable, but the errors may indeed be large. The real errors might even be worse than the estimates.
You eliminated the last point in the calculations of the residuals, but not in the fit itself. You can't do that, because the last point affects the fit. I would dump the last point altogether.