Arc-disjoint hamiltonian paths in 2-generated Cayley digraphs of finite abelian groups

Let $G$ be a finite abelian group, and let $\{a,b\}$ be a $2$-element generating set of $G$ whose elements $a$ and $b$ are nontrivial. Write

$$\mathop{\mathsf{C}\mkern-1mu\overrightarrow{\mathsf{ay}}}(G;a,b)$$

for the directed Cayley graph with generators $a$ and $b$.

Finite abelian Cayley-digraph conjecture. The digraph $\mathop{\mathsf{C}\mkern-1mu\overrightarrow{\mathsf{ay}}}(G;a,b)$ has two arc-disjoint hamiltonian paths.

This conjecture extends the result for Cartesian products of two directed cycles to finite abelian groups. The supplied text presents it as a natural expected extension, but gives no resolution for the full stated generality.