Schleimer's distance formula conjecture for multiarc and curve graphs

Let $\Sigma$ be a compact, connected, orientable surface, and let $\mathcal A$ be a multiarc and curve graph on $\Sigma$. For a witness $W$, let $\pi_W:\mathcal A\to 2^{\mathcal C W}\setminus\{\varnothing\}$ be subsurface projection and define

$$d_W(a,b)=\operatorname{diam}_{\mathcal C W}(\pi_W(a)\cup\pi_W(b)).$$

Let $\mathscr X$ denote the collection of witnesses of $\mathcal A$, let $[x]_C$ denote the thresholded quantity used in the distance formula, and write $d_{\mathcal A}(a,b)\stackrel{K,E}{=}r$ when the two quantities are equivalent up to multiplicative constant $K$ and additive constant $E$. Assume that $(a,b)\in E(\mathcal A)$ if and only if $i(a,b)\leq M$ for some $M\geq0$. Schleimer's distance formula conjecture. There exists $C'=C'(\mathcal A)$ such that for every $C>C'$, there are constants $K,E\geq0$ satisfying

$$d_{\mathcal A}(a,b)\stackrel{K,E}{=}\sum_{W\in\mathscr X}[d_W(a,b)]_C.$$

This is a proposed Masur--Minsky-style distance formula for multiarc and curve graphs. The source does not specify whether it has been proved or disproved.