I had the same issue once with one of my 7mags.I was using RCBS dies.I bought another set of RCBS dies,set them up the same and the brass chambered without any problems.Now as for the Nosler brass,I bought some 30-06 brass once.I could not chamber the brass in my 30-06 without resizing it first.Once I ran it through my dies,it was fine.I use Lee dies for my 338-06 too.When I make my brass for my 338-06,I use once-fired 30-06 brass,usually Winchester brass.I've never had an issue with my brass.You might be getting some spring back on your Nosler brass.If you can get some once-fired 30-06 brass of a different brand,try making some 338-06 brass and see if your still having the same issue.

~Molɔ̀ːn Labé Skýla~
As Bob Hagel would say"You should not use a rifle that will kill an animal when everything goes right; you should use one that will do the job when everything goes wrong."Good words of wisdom...............