I think its more fun to consider several suspects even if Jane "was at the mental house when a rj murder happend." I like to play with the idea.

So, IF, repating if! Jane is red john, then I think Kirkland jobs for himself, not RJ-jane. Obviously. And the handshake thing is a bluff.

I've got two important questions if Jane is RJ.

1. Does his accomplices know that RJ is Jane, do they know his face?
2. He had to start of as RJ young, what led to the murder of his wife and daughter, and what kicked him into become RJ?

I don't think Jane is RJ, but if he is that would be great fun.
This questions can also be asked without any suspects.