Stock pricing with cross ownership
The way I would think of this is as follows. Let us write the value
of the first company as $V_{A}$and the second as $V_{B}.$ Given
your definition, let me know if you agree with the following argument:
$$
V_{A}=s_{AA}\sum_{t=0}^{\infty}\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}\pi_{tB}
$$
 Where $s_{AA}$ denotes the time invariant share of company A that
comapny A owns and $s_{BA}$ denotes the share of the company B that
A owns. Moreover, $\pi_{t}=A_{t}-L_{t}$ or the equity of each company.
By a symmetric argument, we have that :
$$
V_{B}=(1-s_{AA})\sum_{t=0}^{\infty}\pi_{tA}+(1-s_{AB})\sum_{t=0}^{\infty}\pi_{tB}
$$

Now, consider company $A.$ Taking differentials:
$$
dV_{A}=s_{AA}\sum_{t=0}^{\infty}d\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}d\pi_{tB}
$$
Ceteris Paribus,you claim that $\sum_{t=0}^{\infty}d\pi_{tA}=1$
and the other term equals 0. So what you have then is:
$$
dV_{A}=s_{AA}\times1
$$
and 
$$
dV_{B}=(1-s_{AA})\times1
$$
The answer is fairly intuitive- the change in value of each firm is
the change in profits that one of the firms has experienced times
the share of the profitable firm owned by either. 
If each firm owned half, then the change in the value of each firm for an increase in $1 would be half, since each firm would have half the claim on the firm whose profit has increased by a half.