Both Norma and Hornady make 404j brass, know that is not the answer you are looking for. I use the norma for my 404j and 416 Rigby and really like it. I would be interested to hear how you reshape the brass, as 404 cases have a long neck.
Does the 338 edge and rum use/start with same case? If so would really like to hear how your reforming goes, as I am having a 338rum being built and would like to use something other than rem brass.