Connection between Gibbs Energy of Formation and Gibbs Energy of Mixing
Thanks for the links in the comments above. The second one J Chem Thermo, 37, 97 (2005) seemed to be clearer. Eqn (12) reads 
$$\Delta_M G=\Delta_f G^\circ /4
$$ 
but is preceded by the sentence 


  According to the definition of the molar free energy of mixing,
  $\Delta_M G$ for Ni$_3$Al would refer to the formula
  Ni$_{3/4}$Al$_{1/4}$, and thus the equation ... was obtained.


In the first link J Electrochem Soc, 128, 1181 (1981) it is harder to spot your equation. However, I think I see it, in comparing eqns [7] and [10] which relate $\Delta G_m$ and $\Delta G_f^\circ$ to a Coulombic titration expression involving an integral over the compositional variable $y$. This is for the alloy Li$_y$Sn, and the expressions look identical except for a factor $1/(1+y)$. So I guess that's it. However there's no helpful explanation.

Bearing in mind the sentence I quoted from the (2005) paper, I suspect that this factor is simply a question of how these quantities are defined, in relation to the formula of the alloy under consideration (i.e. per atom or per formula unit), and not intimately connected with the expression for the free energy of mixing in terms of mole fractions and activities (except in that it is written per atom, or more accurately, per mole of atoms).

[Edit following OP comment]

I think that this is less complicated than it may have looked. $\Delta G$ is just the difference in Gibbs energy between two well defined states. I see, for instance, on p43 of Statistical Thermodynamics of Alloys by NA Gokcen (1986)
the definition


  The molar Gibbs energy of mixing refers to the process prescribed by
  
  $x_1$ (pure component 1) $+$ $x_2$ (pure component 2) $\rightarrow$ $1$ 
  gram atom of alloy


where, of course, "gram atom" is old terminology; but the meaning is clear. If the original metals are in their standard states, this is essentially the same as the definition of the standard Gibbs free energy of formation of the alloy, except that the latter is usually expressed in terms of one mole of the compound. I think this difference is what is intended by the numerical factor, irrespective of any particular ways of writing the Gibbs energy of mixing in terms of other variables (for example, one can sometimes use regular solution theory to estimate $\Delta S$ and $\Delta H$ of mixing, but I don't think that's relevant here).