It's okay to have some minor variation with villanelle refrain lines! Yes, a very strict interpretation of the format keeps absolutely everything the same in the refrains, but it's very rarely done well (A.E. Stalling's After a Greek proverb's the only one I can think of off the top of my head). I'm a fan of using formats for the effects I can get with them without feeling enslaved to them if I think I can enhance a particular aspect with a minor departure here or there.
Re: another poem named for its form