Weak CMPP conjecture for abelian groups

Let $t$ be a positive integer, let $G$ be an abelian group, and let $A$ be a finite subset of $G\setminus\{0\}$ with $|A|>t$. An ordering of $A$ is a $t$-weak sequencing if its partial sums $s_0,s_1,\ldots,s_{|A|}$ satisfy $s_i\ne s_j$ whenever $i\ne j$ and $|i-j|\leq t$; $A$ is $t$-weak sequenceable if it admits such an ordering.

Weak CMPP conjecture. If

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

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

This is the weak-sequenceability analogue of the CMPP conjecture, proposed after the paper states the corresponding general weak sequenceability conjecture. Its status is not resolved in the supplied text.