Additivity conjecture for hyperbolic volume of annulus-summed swatches

Let $L_1,L_2\subset T^2\times I$ be swatches such that the corresponding links $H\cup f(L_1)\subset S^3$ and $H\cup f(L_2)\subset S^3$ are three-component hyperbolic links. Let $L_1*_mL_2$ denote their meridional annulus sum, and suppose that the corresponding link $H\cup f(L_1*_mL_2)\subset S^3$ is hyperbolic. Hyperbolic-volume additivity conjecture. The hyperbolic volume satisfies

$$\operatorname{vol}\bigl(H\cup f(L_1*_mL_2)\bigr)=\operatorname{vol}\bigl(H\cup f(L_1)\bigr)+\operatorname{vol}\bigl(H\cup f(L_2)\bigr).$$

The conjecture is based on computations suggesting that the algebra induced by meridional annulus sum is additive for three-component links, equivalently for $m\times1$ swatches. The source gives no proof or later resolution.