I don't believe they would tell Palpatine anymore than they have to. They don't like giving up to many Jedi details.... So, to me the Jedi searching for the Sith is something that's under the surface. We know they are looking for them based on TPM... The Jedi are supposed to be wise and make their words few.
However, I would love to see someone render out a vaderesque statue. That's a great idea.. Maybe pulling from some of the old McQuarrie drawings.