You finished in a better place than you started there. Roles are not the answer. As Bateson once said, a role is only a half-assed relationship.
What quickly flattens the hierarchy is to allow the parts to which you refer to overlap, with meaningful participation not only inside them but in the intersections, people participating therefore in multiple parts – relationships between parts implemented via relationships between people. That's how you build networks not only of value delivery (trendy but missing the point) but of strategy and rapid insight/intelligence sharing. It doesn't take much of that to halve the network distance across the organisation.
What quickly flattens the hierarchy is to allow the parts to which you refer to overlap, with meaningful participation not only inside them but in the intersections, people participating therefore in multiple parts – relationships between parts implemented via relationships between people. That's how you build networks not only of value delivery (trendy but missing the point) but of strategy and rapid insight/intelligence sharing. It doesn't take much of that to halve the network distance across the organisation.