Conjecture on Laplace transforms of interference in stationary birth-death networks

Let $\phi_0$ be the point process on $\mathbf{S}$ corresponding to the stationary distribution of $\phi_t$, with intensity $\beta$. Let $\psi$ be an independently marked Poisson Point Process on $\mathbf{S}$ with intensity $\beta$, where the mark of each atom $x$ of $\psi$ is a point $y$ drawn uniformly on the perimeter of a circle of radius $T$ around $x$. For $s>0$, write $I(0;\phi_0)$ and $I(0;\psi)$ for the corresponding interference at the origin. Laplace-transform conjecture. For every $s>0$,

$$\mathbb{E}^{0}_{\phi_0}[e^{-s I(0;\phi_0)}] \leq \mathbb{E}^{0}_{\psi}[e^{-s I(0;\psi)}].$$

This conjectured comparison of Laplace transforms is intended to establish that the Poisson-heuristic intensity $\beta_f$ is a lower bound on the stationary intensity $\beta$; the source provides no resolution of the conjecture.