Maximal $m$-palindromic density conjecture

Let $m\in\mathbb{N}$, and let $A\in\mathbb{N}^{\mathbb{N}_0}$ be an $m$-palindromic sequence that is not eventually periodic. Let $d_m([A])$ denote its $m$-palindromic density. For $r,s\in\mathbb{N}$ with $r\not=s$, let $F(m,r,s)$ be the sequence obtained from the Fibonacci sequence by replacing each occurrence of one symbol by $(rm,r)$ and each occurrence of the other by $(sm,s)$, and let $\varphi$ be the golden ratio. Maximal $m$-palindromic density conjecture. For every such $A$, one has

$$d_m([A])\leq\frac{1}{\varphi}.$$

Furthermore,

$$d_m([F(m,r,s)])=\frac{1}{\varphi}.$$

This conjectures that the constructed sequences attain the maximal $m$-palindromic density among non-eventually-periodic $m$-palindromic sequences, extending the known $m=1$ result for the Fibonacci word. The surrounding construction establishes the lower bound for these Fibonacci-derived sequences, while the asserted universal upper bound is the conjectural part.