The normal bushing neck dies sort of top out at 338 caliber.
C4HD and others DO make a large format bushing/die and C4HD does make some .500 OD neck bushings in the .390 range were 375 ctg fall but overall these days finding out if you are ordering an in stock item or ordering for an extended back order is a real PITA. Plus a .500 OD bushing with a .390 ID is pretty darn thin .
So I decided to make my own neck die which uses a .560 OD bushing.
I used a PTG die body, they are pretty cheap overall and it saves some time. They are 4140 steel which has no particular advantage. PTG gets $28 for them, while they do save time I'm kind of thinking next time I might just use some 12L14 for dies that will be left soft.
Here is the partially finished result.
Some of the focus here was "what can I accomplish in a spare hour" and I have a new to me laydown threading insert holder so the threads are not as mirror smooth as I would like, but it works for what we are doing. This is made from 12L14 steel.
I worked out a simple way to make some grasping grooves for the bushing retainer, overall I am not a fan of the knurling process, I like this a lot better, and the coordinates came out to nearly round numbers. To do multiples of this an indexer would make it faster but for 1 I just used the DRO. I plunged those straight down with a 1/4" endmill.
I made a test bushing out of 12L14 steel, it machines like butter, cannot easily hardened but man does it machine nice , and bar ends (leftover from cnc process that use a 12' bar) are cheap on Ebay. Serious long term bushings might be made from say O1 steel and hardened, then lapped perfectly round and to size.