Shibuya's boundary-link conjecture for self Delta-equivalence

Let an oriented link be a boundary link if its components bound pairwise disjoint Seifert surfaces in $S^3$. Let the trivial link be the link whose components are disjoint unknotted circles bounding disjoint disks. Two links are self $\Delta$-equivalent when they are transformed into each other by self delta moves and ambient isotopies, with all three strings in each move belonging to the same component. Shibuya's conjecture. Any boundary link is self $\Delta$-equivalent to the trivial link. This conjecture predicts that self Delta-equivalence detects no further obstruction for boundary links beyond their boundary-link structure; the supplied text gives no resolution.