Back in 1990's, when I worked for a lawyer, it cost $140 just to file your first paper in court and start a court case. I don't even know what it costs now. Add to that the cost of the lawyer (if you can convince a lawyer that you have a copyright to an old piece because you changed a few words, tried some new chords or used new instruments.)

After that, most likely the judge will throw your case out of court, basically saying, "Don't waste our time."

There is no penalty for claiming a copyright that you aren't really entitled to, so people do it all the time. But when you get right down to it, nobody bothers to enforce these claims in court and they are meaningless.
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I was just working with a carol from Dorset called 'Shepherds Arise.' Some guy made a MIDI of it by copying the four parts note-for-note from a book published in 1926. He assigned instrument sounds to the lines (organ for one line, French horn for another, etc.) Then he claimed he had a copyright on the song. Horsefeathers.

The overworked, overbooked courts of this world deal with big money, serious injuries, and life & death. They cannot be bothered with guys who spent an hour tinkering with a public domain song.