Uniform-speed conjecture for a non-escaping impurity in TASEP

Let an impurity in the totally asymmetric simple exclusion process have jumping rates $b1$ and $b2$, and initially be located at the interface of a $1$-$0$ profile. Assume that $b1+b2 ot<1$ and condition on the impurity not escaping the rarefaction fan. Uniform-speed conjecture. The asymptotic speed of the impurity is uniformly distributed over the interval

$$[\max(-1,1-2b2),\min(1,2b1-1)].$$

For $b1>1$ or $b2>1$, the impurity can escape from the rarefaction fan and acquire speed $b1$ or $-b2$, respectively; determining the conditional non-uniform distributions remains an open problem, while numerical evidence supports the stated uniform law.