I tried resetting and fitting again:

    for i in range(5):
        if PLOT_GUESSED_LORENTZIAN:
            vib_plot(None, freq_axis, psd_data, A_guess, B_guess, C_guess,
                     minFreq, maxFreq, plotVerbose=True)
        g("A=%g; B=%g; C=%g" % (A_guess, B_guess, C_guess))
        g("fit f(x) '%s' via A,B,C" % datafilename)
        A=abs(float(g.getvar('A'))) # A and B only show up as squares in f(x)   
        B=abs(float(g.getvar('B'))) # so ensure we get positive values          
        C=float(g.getvar('C'))
        A_guess = A
        B_guess = B
        C_guess = C
 
But the extra fit cycles had no effect ("After 1 iterations the fit
converged." with no real parameter change.).