Hadn't thought of that Rod. Good idea and one I'd certainly do.
I have a set of CH4D .358 swage dies for handgun bullets that would work. back in the late 70's, I used them to actually swage some .375's down to .358 and it worked - also broke the Rock Chucker. Sizing the Privi down to .358 would be a snap with a couple stages in Lee's $25.00 custom sizer dies, say .361" and .357or8.

Sizing (drawing) the bullet down also seems to toughen the jackets slightly, which is a good thing. The 270gr. Speer is another I'd most certainly try. 2,450fps with that one in a standard Whelen would be a good ctg. for North America, I'd expect. or 2,600fps in an Improved case. Of course, drawing or sizing opens the door for a bunch of other bullets - 232gr. Vulcan or Oryx and all the other 285/6gr. bullets too.