Your process is similar to ours, only flipped:
We have the Project Managers manage all routings with the Designer simply providing the PDF to be routed either via email or in the Documents area; but Designers do not themselves start, manage, or participate in PHQ routings.
The back-n-forth between design and Project Management before formal review with the clients and process departments is done outside Workfront for speed. We only use PHQ for routings that need decisions and sign-offs.
We find it better not to bog-down design and production with managing PHQ routings and to let the PM manage it so they can make decisions and guide direction before handing back to the designers.
We also don't use the Versions ability, at least not yet, so every subsequent routing is "new" to avoid confusion. Our deployment is new and while versioning has some serious benefits, the complexity was too much for launch. Although the more I stare at reporting for PHQ, I think the log trail is more clear when routings are stand-alone as well (for legal purposes).