If you're keeping it private, none of this applies. I'm talking about "hey that project is bad, I am now maintaining a competing project, please use it instead."
Instead of framing it as "that project is objectively bad, my one is better", why not say "my project is a fork of this project but with a bit less unsafe" and then see what the community does?
Forking isn't provocative. Forking and then claiming your fork is objectively superior is.