With respect to anybody's concern about 'being compromised' online, I have a different reality and feel as a career musician. Unfortunately I feel the OP was led astray and to be overly cautious to the point of diminished returns. I personally don't find it to be sound advice as it is too incomplete. Protection is always wise, but there is a reality to new real-time reality to that.

When I want to 'protect' my songs today, I post them online and leave them. I have 2 places for this.
This is what is called 'publishing'. Self publishing and online publishing, but published nonetheless.
This creates a date/time stamp that is easily verified by the 2 hosts. Youtube is the best for this IMO even though I don't use it.

If I found someone 'stealing' my tune or a vital 'hook' well I have a course of action. I also have my tunes copy written the old fashioned way. But in the end, online publishing is the fastest and most secure outside of a known single or major artist.

If you don't post online now, where do you showcase your material?

Of course all of our work is subject to plagiarism today. One irony here anyway is that few on this board aren't using BIAB for the majority of their tracks (ie; not your work anyway)and second, few artist ANYWHERE are doing something so off the beaten path that it would not be some type of plagiarism. And if that were the case, those artists wouldn't be listened too much anyway. What isn't plagiarized? If you want your song to be liked, it better be familiar to some part of our culture. At the least it is familiar to you.

Want to protect your work? Post it online, release a disc, copyright it. Still won't be safe. Ever.
I hope you can enjoy the art more and the fear less. It really isn't such a cut throat business as it is far more transparent than before. Heres a challenge: Try to even GIVE one of your songs away to somebody who can use it for profit. Try. It is a lot harder than you may imagine.

Cheers and blessings.