Double Slab conjecture for very long three-tori

Let $T^3$ be a very long flat three-torus, obtained by stretching one or more directions of the cubic torus, and consider its double-bubble problem.

Very-long-torus Double Slab conjecture. In the special case of a very long $T^3$, the Double Slab is optimal for most volumes.

The claim concerns how changing the shape of the torus changes the phase diagram. It is presented as a conjecture without proof.