I too have heard that mailing to yourself is chancy at best. I don't know for sure (i.e. this is not legal advice, does not establish a lawyer-client relationship, I am not a lawyer, etc.) but maybe getting your lead sheet notarized is an alternative way to create a record of your authorship, if you don't want to spend the fee to register the copyright.

Registering the copyright appears to have certain legal advantages, see 17 U.S.C. 411,412.