Conjecture on Brieskorn homology spheres from regular Lagrangian slice knots

Let $\Sigma(p,q,r)$ be a non-trivial Brieskorn homology sphere, let $n$ be a natural number, and let $K$ be a regular Lagrangian slice knot. Lagrangian-surgery conjecture. No such $\Sigma(p,q,r)$ can be obtained as smooth $\frac{1}{n}$ surgery on $K$. This is presented as a weaker conjecture motivated by Gompf's conjecture and the preceding theorem on surgery along regular Lagrangian slice knots; the source gives no resolution.