Conjecture on the equivalence of overconvergent and surcoherent F-isocrystals

Let $X$ be a $k$-variety, let $Y$ be a smooth open of $X$, and suppose that $(Y,X)$ is $d$-embeddable. Write $(F\text{-})\operatorname{Isoc}^{\dag}(Y,X/K)$ for the category of overconvergent $F$-isocrystals and $(F\text{-})\operatorname{Isoc}^{\dag\dag}(Y,X/K)$ for the category of surcoherent $F$-isocrystals.

Equivalence conjecture. There is a canonical equivalence of categories

$$(F\text{-})\operatorname{Isoc}^{\dag}(Y,X/K)\cong (F\text{-})\operatorname{Isoc}^{\dag\dag}(Y,X/K).$$

This is presented as the analogue of the corresponding result for smooth varieties. It would identify the overconvergent and surcoherent theories for every $d$-embeddable pair, but the source gives no resolution.