Conjecture that Koschorke's and Milnor-type invariants agree for Brunnian embedded links

Let $f$ be a $\b7$-Brunnian embedded link with components indexed by $\b7$, and let $\b7$ be a permutation of the first $d-1$ component indices. Write $\b7_\b7(f)$ for Koschorke's invariant and $\b7(\b7(1),\ldots,\b7(d-1),d)$ for the invariant introduced in the paper.

Invariant agreement conjecture. For $\b7$-Brunnian embedded links, Koschorke's $\b7_\b7(f)$ coincides up to sign with $\b7(\b7(1),\ldots,\b7(d-1),d)$.

The agreement is known in particular when all components have codimension at least $3$, and in the case $m=3$, where both invariants coincide, up to a sign depending only on $d$, with Milnor's classical invariants. The conjecture concerns the remaining cases, especially links involving codimension-$2$ components, where these invariants are not known to be complete link-homotopy invariants.