Change the ComboBox Popup control to be right-aligned with the its parent

Question

I'm trying to get a ComboBox to display its Popup right aligned rather than left-aligned as is the default. I mean I want the right edge of the Popup to be aligned with the right edge of its parent.

I tried overriding the ComboBox class but that didn't quite work as the Popup HorizontalOffset seems to be reset somehow. I thought that would be a fairly easy change but I can't find any resource talking about this issur.