I just stumbled on this video showing a home made contraption to remove spent Berdan primers from rifle cases. Simply stated, the key is to use an offset primer punch that fits into an empty case with the 0.8mm offset punch tip going though a flash hole to push the primer out.
This is the slickest setup I've seen to date! The video's author is a genius.
Here is where the above video's author acquired the offset primer punch: http://www.frankonia.de/Berdan+Aussto%C3%9Ferstift/Ansicht.html?Artikelnummer=93491&page=2&navCategoryId=62816