The GEI conjecture for generic derivations over rosy algebraically bounded theories

Let $T$ be a rosy and algebraically bounded theory extending the theory of fields of characteristic zero. Let $\Delta$ be a finite tuple of derivations, and let $T^{\Delta}_g$ and $T^{\Delta,\operatorname{nc}}_g$ denote the model completions for commuting and not necessarily commuting derivations, respectively. Write GEI for geometric elimination of imaginaries.

Generic-derivation GEI conjecture. The theories

$$T^{\Delta}_g \quad\text{and}\quad T^{\Delta,\operatorname{nc}}_g$$

have GEI.

This is a weaker conjecture than the general GEI transfer conjecture and would remove the GEI assumptions from the relevant rank and rosiness results. The source gives no resolution, so the conjecture remains open.