Equilibrium with Externalities: Solving without FOC
It is my impression that there is an inconsistency here.  

If firms want to maximize $V(n)$ which is some "surplus revenue over costs" function, then surplus they will produce. Meaning, that this surplus/profits cannot be given to workers, in the form of wages, because wages are cost. It may be given as dividends or, say, end-year bonus, but in any case it won't be related to $n$.
So we do not have $Y=wn$ but rather $Y = wn + d$, and the externality appears to break down.

The $Y=wn$ relation is consistent with a "non-profit" organization, which would demand as much $n$ as needed in order to have zero profits. In such a case, the wage would be equal to the average product of labor, not the marginal one.