The Borel bireducibility conjecture for consecutive-rank torsion-free abelian groups

For each $n\geq 1$, let $\cong_n$ be the isomorphism relation on the space of torsion-free abelian groups of rank $n$, and let $\cong_{n+1}^+$ be the corresponding relation with the positive superscript. The consecutive-rank bireducibility conjecture. For every $n\geq 1$,

$$\cong_n\sim_B\cong_{n+1}^+.$$

This would identify the Borel complexity of the rank-$n$ classification problem with that of the positive variant in rank $n+1$. The source presents the assertion as plausible based on earlier reductions, but gives no resolution.