Definitely could work. Just start the seven times from the fall of Bablyon and release of the Jews. Say "God released them in 537, but by not restablishing his kingly line showed in 537 that the gentile times has started." Most JWs would miss the whole irony of a 1984 start date. Why 1984, because it was 3.5 years after Ray Franz had been removed and the temple cleansed. Jesus arrived in 1984 to find the organisation clean. A better argument than 1919, since at least in 1984 there was a Governing Body.
Don't give them ideas. That '3.5 years after Franz' stuff might actually seem plausible to them.
The Jews actually returned in 538, but they've never let facts bother them anyway.