Biased Glauber dynamics conjecture for even-degree regular trees

Let $T$ be a regular tree of even degree, and let the initial spin configuration have a product distribution whose Bernoulli marginals are biased. Consider zero-temperature Glauber dynamics on $T$. Biased Glauber dynamics conjecture. The dynamics freezes almost surely to a configuration in which all spins are the same. This conjecture concerns the effect of a biased initial distribution in the even-degree regular-tree case; the corresponding symmetric product-distribution dynamics is known not to freeze almost surely, while simulations for the simultaneous-clock model support the biased case stated here.