Files with the same name in your mod should override the ones in the Shared. So one thing you could try is to add empty files to your mod with the same name as the ones you want to get rid of. Or you could maybe add copies of one for a race you do want to keep with the same name as the ones you want to hide (no idea if that will add this race multiple times though).
Yeah, I did try that trick of making copies and renaming the fields but as you theorized, it made additional copies of the race. I have not tried empty files though, so I'll see what that does.
Ironically, the challenge ended up changing how I want to do character creation anyway so I think I have a workaround, but I do want to know if this works so I will give it a shot. Thanks for the feedback!