Explicit Maurer–Cartan element in the log Calabi–Yau case

Assume the log Calabi–Yau condition, so that $\lambda_i=2$ for every divisor component, and assume the minimal Chern number of $M$ is at least $2$. For each $i$, let $B_i$ be the cocycle obtained by counting caps through $D_i$, and set

$$B:=\sum_i e^{\lambda_i}\cdot B_i.$$

Let $\beta$ be the Maurer–Cartan element from the deformation conjecture. Splitting conjecture.

$$\beta=B.$$

This predicts that no additional terms occur under the stated grading and Chern-number assumptions; the source gives evidence and discusses possible extensions, but the claim remains open.