Sorry, I am a bit late to the party,
I have .404 Express built by Barnes. It is built a standard 98 Mauser action. I acquired it 25-30 years ago.
I started shooting with .411 bullet, but it didn't shoot well. I had a difficult time then finding .411 bullets. I decided to get a bullet mould and shoot cast bullets. I slugged the bore and it measured at .416" groove.
I was talking with the late "Chick" Donnelly about the gun and cartridge and he suggested I measure the fired brass. He also said compare that with the .416 Chatfield-Taylor, later just .416 Taylor. I found that the .404 Barnes Express (Barnes-Jones Express) had a shoulder a few thousandth smaller than the Taylor, other wise they were the same. Basically Chatfield-Taylor copied the Barnes-Jones cartridge. He perceived a need for a lightly large shoulder, but I don't recall what that was. What ever it was his cartridge was pretty successful.
A friend had a .416 Taylor. My .404 Barnes brass would load and fire in his chamber. His .416 Taylor cartridges would not chamber in my gun.
I use .416 Taylor Load data. I had Whidden build me dies.
https://www.whiddengunworks.com/
I haven't used this gun in years- 2002 maybe. I usually get rid of guns I don't use much. That is, unless they shoot well, those guns i keep.
I would have to dig out an old laptop or old back up drive to find my load data.
Suggest you slug you bore an make sure you are .411 groove,