Shadow-diagram move conjecture for surface-links

Let $\mathfrak D^1$ and $\mathfrak D^2$ be shadow diagrams for a fixed surface-link $(X,\mathcal F)$. The allowed moves are core stabilization or destabilization, Hopf stabilization or destabilization, relative double twist, interior perturbation or deperturbation, Markov perturbation or deperturbation, arc and curve slides, and isotopy rel-$\partial$.

Shadow-diagram move conjecture. The diagrams $\mathfrak D^1$ and $\mathfrak D^2$ can be related by a finite sequence of moves, each of which is one of the listed types.

This is presented as a diagrammatic analogue of the stabilization and perturbation conjecture for bridge trisections. It would give a finite move-set relating any two shadow diagrams of the same surface-link, but the source does not prove it.