Flory–Schulz type distribution with stoichiometric imbalance
I came up with a way to solve my own problem as I was writing my question, but I feel as though it is a bit hand-wavy.  I would appreciate any input regarding the validity of this solution.  

The following is a workaround to force the Flory distribution to have a maximum value that is consistent with the average degree of polymerization due to stoichiometric imbalance via Carothers' equation.  Carothers' equation models how stoichiometric functional group imbalances limit the average degree of polymerization for the step-growth mechanism.  This average degree of polymerization $(\text{DP}_\text{average})$ can be calculated very simply:

$$\begin{align}
\text{DP}_\text{average} &amp;= \frac{r+1}{r+1-2rp} \\
\end{align}$$

When there are no stoichiometric imbalances, and the Flory distribution is valid:

$$\text{DP}_\text{average} = \frac{1}{1-p}\\
f(\text{DP}_\text{average}) = x \cdot p^{x-1} \cdot (p-1)^2$$

Let $p_\text{eff}$ be the effective extent of reaction, which is related to $r$ and $p$ via:

$$\frac{1}{1-p_\text{eff}} = \text{DP}_\text{average} = \frac{1+r}{1+r-2rp}\\
p_\text{eff} = 1 - \frac{1+r-2rp}{1+r}$$

This $p_\text{eff}$ can be used to calculate the ideal Flory distribution according to

$$F(\text{DP}_\text{average}) = x \cdot p_\text{eff}^{x-1} \cdot (p_\text{eff}-1)^2$$

The function $F(\text{DP}_\text{average})$ will force the molecular weight distribution to be properly centered about the  $\text{DP}_\text{average}$ that is consistent with Carothers' equation.  I'm not sure if this is chemically sensible, or accurately describes a real-ish polymer system.  Comments/alternative answers would be appreciated.