Connected sum formula for bent complexes in instanton Floer homology

Let $K_i\subset Y_i$ for $i=1,2$ be rationally null-homologous knots. Write $K_1\# K_2$ for their connected sum, and let $B^\pm(K)$ denote the bent complexes associated to a knot $K$. Connected sum conjecture for bent complexes. There exist chain homotopy equivalences

$$B^\pm(K_1\# K_2)\simeq B^\pm(K_1)\otimes B^\pm(K_2).$$

This would provide a stronger connected sum formula than the known tensor-product isomorphism for instanton knot Floer homology, by encoding the information in bent complexes. It is motivated by the analogous formula in Heegaard Floer theory and is not resolved in the supplied source.