For Example 2 / Prop 35, would this model also work?

Define $W$ to be the factor corresponding to the question "are the second and third bits equal or not?" Then $\left(\right(\Omega ,\{X,V,W\}),\text{id})$ is a model of $\Omega$. I believe this is consistent with $D$:

For $O=\left\{\right(X,V,\left\{\Omega \right\}),(X,Z,Y),(V,Z,Y\left)\right\}$:

We have $h^F\left(X\right)=\left\{X\right\}$ and $h^F\left(V\right)=\left\{V\right\}$ for the first condition.

We have $h^F(X\mid Y)=\left\{X\right\}$ and $h^F(Z\mid Y)=\left\{W\right\}$ for the second condition.

We have $h^F(V\mid Y)=\left\{V\right\}$ and $h^F(Z\mid Y)=\left\{W\right\}$ for the third condition.

For $N=\left\{\right(X,Z,\left\{\Omega \right\}),(V,Z,\left\{\Omega \right\}),(Z,Z,Y\left)\right\}$.

We have $h^F\left(Z\right)=\{X,V,W\}$ for the first and second conditions.

We have $h^F(Z\mid Y)=\left\{W\right\}$ for the third condition.