Unless I'm miscounting, you have three ways to go:
1. Buy a bare #6 Bock nib and use the feed that comes with the Churchill. I can't speak to whether the nib fits the feed well or whether it will work well if it does fit.
2. Modify the section of the Churchill to use the Bock feed housing. This should be fairly simple as the Churchill feed fits directly into the section without a housing. If you want to screw the housing in, taps are available to match the Bock threading from Classic Nib. Otherwise you can glue the housing into the section. If you use shellac to glue it in, you can remove it with heat. If you screw up the section, replacement section/feed/nib assemblies are available directly from Berea Hardwoods. The assembly is referred to as El Grande Nib.
3. Make the section yourself. The section/barrel thread is M10-1.
Disclaimer: It's possible that things have changed. I haven't made a Churchill for a few years
Best of luck,
Bill