The collapse conjecture for the sutured-annular-to-Khovanov spectral sequence

Let $W_k$ denote the invariants in the decomposition associated with the spectral sequence from sutured annular Khovanov homology to ordinary Khovanov homology. Collapse conjecture. The spectral sequence collapses immediately, and

$$W_k=0\qquad\text{for all }k\geq2.$$

The conjecture predicts that no higher invariants survive beyond the immediate page of the spectral sequence. The supplied text gives no resolution or further evidence about its status.