Nonexistence of simultaneously $d_2$-minimal and $d_2$-HI Banach spaces

For a finite-dimensional Banach space $F$, let $d_2(F)$ denote its Banach–Mazur distance to the Euclidean space of the same dimension. A Banach space is $d_2$-minimal if it has the corresponding minimality property, and $d_2$-HI if it has the corresponding hereditarily indecomposable property. $d_2$-minimal/$d_2$-HI conjecture. A Banach space cannot be simultaneously $d_2$-minimal and $d_2$-HI. The conjecture is presented as a stronger form of the negative answer to whether a non-ergodic Banach space can be simultaneously $d_2$-minimal and $d_2$-HI. The source does not state a resolution.