Monotonicity conjecture for the speed of once-reinforced walk on regular trees

Let $d$ be fixed, and consider the once-reinforced walk on a $d$-regular tree with forward-edge weights $u_0$ before reinforcement and $u_1$ after reinforcement. Monotonicity conjecture. The speed given in the cited speed theorem is monotone increasing in both $u_1$ and $u_0$, and is strictly monotone in the transient regime. The conjecture concerns how the asymptotic speed depends on the two reinforcement weights on regular trees; the source provides no resolution of this expectation.