Existence of virtually equivalent, non-isotopic knotted spheres

Let $n\geq 2$. A knotted $n$-sphere is an embedded $S^n$ in $D^{n+1}\times [0,1]$, and two such knots are virtually equivalent when they become equivalent after the allowed virtual replacements. Existence conjecture. There are knotted $n$-spheres in $D^{n+1}\times [0,1]$ which are virtually equivalent but not classically isotopic. The preceding examples involve knotted tori, while it remains open whether analogous examples exist for knotted spheres; the conjecture proposes such examples in every dimension covered by $n\geq 2$.