What's the effect of changing the ordinal index of ranks to Scott ordinals, on the consistency strength of Zermelo + Ranks + Ordinals?

Question

This question is about indexing the stages of the cumulative hierarchy in Zermelo set theory $``\sf Z"$

Now if we add to $\sf Z$ the following two axioms:

Ranks: $\forall x \exists \alpha : x \in V_\alpha$

Ordinals: $\forall \text{ well-ordered }x \, \exists \ \text{ordinal } \alpha \, \exists f \, (f: x \hookrightarrow \{\beta: \beta < \alpha\}) $

Now if ordinal in the above formulations stands for von Neumanns, then the theory has a consistency strength strictly more than that of $\sf Z$.

If we take those to be Scott's ordinals instead, then would the resulting theory still be of more consistency strength than $\sf Z$