CMPP conjecture on sequenceability with no opposite pair

Let $G$ be an abelian group and let $A$ be a finite subset of $G\setminus\{0\}$. A subset is sequenceable if it admits an ordering whose partial sums are distinct, except that the initial and final partial sums may coincide.

CMPP conjecture. If

$$|A\cap\{x,-x\}|\leq 1$$

for every $x\in G$, then $A$ is sequenceable.

This is a weaker version of the Alspach–Liversidge conjecture, presented by Costa, Morini, Pasotti, and Pellegrini for applications to Heffter arrays. The source notes that the earlier formulation included the additional hypothesis $\Sigma A=0$; the paper uses the stated slightly more general version, and does not report a resolution.