The variant of the Leinster–Willerton conjecture for magnitude and intrinsic volumes

Let $n>0$, let $X\subseteq\mathbb{R}^n$ be a compact convex subset, let $\mathcal{M}_X(R)$ denote its magnitude at scale $R$, and let $V_k(X)$ be its $k$-th intrinsic volume.

Variant of the Leinster–Willerton conjecture. There are universal constants $\gamma_{0,n},\gamma_{1,n},\ldots,\gamma_{n,n}$ such that, for every such $X$,

$$\mathcal{M}_X(R)=\sum_{k=0}^n\gamma_{k,n}V_k(X)R^k+o(1),\qquad\text{as }R\to\infty.$$

The conjecture would extend the relation between magnitude and intrinsic volumes beyond the coefficients already known, and in particular would show that the constant-order term is proportional to the Euler characteristic $V_0$.