If you know $p_0|_{z=1}=1$ and $p_1|_{z=1}=0$ and you want to know $p_0'|_{z=0}$ and $p_1'|_{z=0}$, you don't need a shooting method.

Just use ODE45 as you already did and define tspan=[1 0]. This way, you integrate back in z-direction from z=1 to z=0. Once you have reached z=0,

$p_0'|_{z=0}=-\dfrac{32 \beta}{R^4}/p_0$

and

$p_1'|_{z=0}=(-\dfrac{2-\sigma_v}{\sigma_v}\dfrac{8}{R}p_0'-p_0'*p_1)/p_0$

Best wishes

Torsten.