Longest-game conjecture for the Split Smallest strategy

A Zeckendorf game on $n$ consists of legal combining and splitting moves applied to the Zeckendorf decomposition of $n$. The Split Smallest deterministic game applies moves by splitting from smallest to largest, after which it adds consecutive indices from smallest to largest.

Longest-game conjecture. The longest game on any $n$ is achieved by applying splitting moves whenever possible: first adding $1$'s, then splitting from smallest to largest, and finally adding consecutive indices from smallest to largest. The source also identifies Split Smallest, which instead splits from smallest to largest before adding $1$'s and then adding consecutive indices from smallest to largest, as another candidate for a longest possible game.

The statement is presented as an earlier conjecture, while the paper describes Split Smallest as another candidate and does not report a resolution of either claim.