All I can offer here is that my RCBS 357 Cowboy sizing die sizes my cases to .374 OD, which is just slightly under the dimension at the base "as fired". The 1/4 inch or so above the rim doesn't get toughed by the sizing ring at all.
I used to have the dimensions written down for cases sized down in my old Hornady Durachrome 357 mag sizing die. I can't find it now of course, but I do remember that the case was distinctly tapered from base to case mouth. You could easily see it. I'll have to see if I can find the die again, it's around here somewhere.