Costa–Morini–Pasotti–Pellegrini restricted rotational sequencing conjecture

Let $G$ be an abelian group and let $S$ be a finite subset of $G\setminus\{0\}$ such that

$$\Sigma S=0$$

and $|S\cap\{x,-x\}|\leq1$ for every $x\in G$. Costa–Morini–Pasotti–Pellegrini conjecture. Then $S$ has a rotational sequencing. This weaker conjecture than the main strong sequenceability conjecture is sufficient for some applications to Heffter arrays; the supplied status evidence does not resolve it.