Undecidability conjecture for epimorphisms onto finitely generated virtually Abelian groups

A finitely generated virtually Abelian group is a finitely generated group containing an Abelian subgroup of finite index. The uniform epimorphism problem onto a class of groups asks, given a finitely presented group and a target class, whether the group admits an epimorphism onto some group in that class.

Undecidability conjecture. The uniform epimorphism problem onto the class of all finitely generated virtually Abelian groups is not decidable.

The question is motivated by the decidability of the problem for finite and Abelian targets, contrasted with the partial positive results for direct products of finitely generated Abelian groups with finite groups and for virtually cyclic groups. The source presents the asserted undecidability as plausible; no resolution is supplied there.