This probably isn't what you want to hear and you probably already know but small copper machine screws can be pretty difficult to find in specific sizes, from what I have gathered it seems that many places either machine them in house or have them machined in bulk for their own specific use, I was going to recommend brass but it appears you have already reached the same conclusion, brass is much easier to find.
I needed a specific copper 510 screw as well for a clone Zenith V2, nothing I could find in copper was the correct pitch and length so I decided to go a different route, I made one out of a solid copper rivet.
Weaver Leather Assorted Copper Rivets and Burrs (#9) - For Life Out Here I was in a situation where it was actually easier for me to make two screws out of those rivets, using the correct thread-die on the shaft and cutting a flat-head in to the rivet base after I reduced the size. For what it's worth I have even used those copper rivets to entirely replace a 510 center post with a one-piece unit, they can work for numerous
vape applications if you've got an open mind and some tools.