If you created your own arrangement of a PD tune, you would actually own the copyright. People would need to come to you for permission to use the work. They would need to obtain a sync license, mechanical license from you.
Just ask the good folks at G Schirmer / Music Sales who've made a fortune off of dead composers and so-called "arrangements" of PD works. They charge an arm and a leg to license these arrangements for the use in videos.
Something about this loophole in copyright and the monetization of dead composers, just seems copywrong. Mozart is likely rolling over in his grave.