This is the approach I want to take as well - but I give up so many times because I can’t track down a method of communicating with that person. I looked a while ago and I couldn’t find a way to send a message to a user on GitHub. Any recommendations on effective ways of reaching out to project owners?

It's usually fine to open an issue on the repo. It should have a detailed description of what's wrong, reproduction steps if appropriate etc, basically enough to show that you know what you're doing, have put some effort into it, and care about the project. Perhaps you'll get a response from a project maintainer, and can ask if they're open to a PR to fix it. IME, there's pretty good chances of positive engagement and eventual PR merge if you're fixing an actual bug in a good way, and not trying to add some massive new feature or completely change the way the thing works or something.

If it's excessively difficult to find a way to communicate with a project maintainer, well, maybe there's your sign that this is not a good project to contribute to.