I like a hybrid of the public and private voting.
For the original 1 through 15 voting, I would like to keep that private. At the same time, I'd prefer to see the actual playoff rounds voted on publicly.
I think the voting process was a little hard for some people. While sending a PM sounds easy enough, I think studies have shown that if people have to take even a small extra step, they become avoidant. It's just easier going to a public thread, and posting your choice.
Of course, there's good and bad with that. The good is, GMs know who they should be lobbying, etc., since they have yet to vote. The bad thing is, it can cause tension and hurt feelings, sidetracking debates.