Harmonic-radius bound for epsilon-acK manifolds

Let $\epsilon\in(0,a]$, and consider $\epsilon$-acK manifolds with parameters $(n,d,k,i_0,a)$. Harmonic-radius conjecture. The $W^{2,p}$ harmonic radius is uniformly bounded below in terms of $(n,d,k,i_0,a)$. The question is motivated by Anderson's question about curvature concentration and is proposed specifically for the almost-complex Kähler setting; the source gives no resolution.