The vector of residuals that you proposed as superior method did not give give satisfactory results with Minerr
Well, it should do. It should in fact give superior results. If you calculate the SSE after the fit using both methods, what numbers do you get?
Also, your short-hand version for generating the vector of residuals did not work. I had to program a subroutine with a for-loop to generate the vector.
Without the data I had to make some guesses there. It's usually possible to get the vector of residuals with some sort of vectorization, and then the minimization is faster than if they are calculated using a program. I do have cases myself where I had to resort to a program though.