You definitely own the copyright of your own recording and playing of a tune in the puplic domain. It's not fair use at all. You own the copyright a recording of a classical composition, even if it contains non-copyrighted elements. Fair use implies you're using a copyrighted work in a manner that is protected by the first amendment.
The "this is entirely my work" would apply here since nothing else in the video was legally owned by anyone else. If the option meant quite literally everything in the video was entirely created by me then it would apply to nothing since you could use no language or literally anything inspired by anything.
Maybe I'm wrong, but I had been told that the reason the US added fair use exemptions was to make sure our copyright laws were compatible with the first amendment, or else risk them being struck down.
> Maybe I'm wrong, but I had been told that the reason the US added fair use exemptions was to make sure our copyright laws were compatible with the first amendment
Copyright and free speech contradict each other - copyright is a form of legalized, privatized censorship. You can argue that copyright is OK - but then better take a look in the mirror and don't argue against the censorship in China etc. . Or you can argue against censorship, but then you must argue against copyright, too.
Regardless of whether that is true, if law is modified for a specific purpose, that does not imply that its effects are limited to that specific purpose. If fair use was added to ensure copyright law would not violate the first amendment, it is still possible that fair use covers more than is protected by the first amendment.