Great post. I like the closing:

    Ultimately, we decided the best thing to do was to do nothing and hope for the best.

All of the experienced network engineers that I've worked with who have run into issues that feel like they can be improved by tweaking QoS somewhat, always end up saying to me, "Nah. Just get a bigger/more pipes." I've never been in a position like yours to make a cogent argument as to why they were wrong, and laid out the details as well as you did there.