Is the random-field Heisenberg chain localized at strong disorder

$H = \sum_i J S_i . S_{i+1} + h_i S^{z}_i$ with h_i independent and uniform in $[-W, W]$. Does a $W_c < \infty$ exist such that for $W > W_c$ infinite-temperature eigenstates obey an area law and local memory of the initial state persists as $t \to \infty$, in the limit $L \to \infty$? Answer yes or no, with an estimate or bound on $W_c$.

A proof for this model (Imbrie's 2016 proof covers a random Ising chain with transverse field and relies on an unproven limited-level-attraction assumption), or numerics that control rare thermal regions at sizes where avalanche effects are visible.