The pervasive view is that, no matter what, project management will insist upon metrics in test reporting. Testers look on in awe at reporting in other areas of the project, where conversations convey valuable information. We are right to feel sad when the reporting sought is a numeric summary.
But they want numbers...Do they? Do your project management really want numbers? I hear often that testers have to report metrics because that is what is demanded by management; that this is how things are in the real world. I don't think this is true at all. Managers want the numbers because that's the only way they know to ask "How is testing going?". If you were to answer that question, as frequently as possible, making testing a transparent activity, much of the demand for numbers would disappear.
"Even if I convince my manager, they still need the numbers for reporting further up the chain". If your manager has a clear picture of where testing is at, then they can summarise this for an executive audience without resorting to numbers. Managers are capable communicators.