Canonical-form conjecture for reduced switches

Let $F_k$ denote the Fibonacci numbers, let $s(n)$ be the switch component appearing in the reduced switch construction, and let $\operatorname{val}(m)$ denote the combinatorial game value of a heap of size $m$. The reduced switch of size $2F_{2n+3}-2$ has the form specified below.

Canonical-form conjecture. For all $n\in\mathbb{N}$,

$$\operatorname{val}(2F_{2n+3}-2)=\{1\mid s(n)\}.$$

The conjecture asserts that the relevant Left option can be replaced by $1$ and that the remaining Left options are dominated or reversible. It is motivated by computations and by the move from a heap of size $2F_{2n+3}-2$ to one of size $F_{2n+3}-1$, but no resolution is supplied here.