Unipotent Selmer dimensions for CM curves via Iwasawa loci

Let $X/\mathbb{Q}$ be a smooth, projective, geometrically integral curve of genus $g \geq 2$ with a point $ b \in X(\mathbb{Q})$ and geometrically CM Jacobian. Fix an odd prime $p$ of good reduction, and let $U$ be the étale pro-unipotent $\mathbb{Q}_p$-fundamental group of $X$. We prove, for all $n