What can I do to stomp out these rumors?

You can keep copies of the emails, go to the VP directly and tell him that while you want to stay with the company, unless he issues a company-wide retraction of his malicious lies and rumors, you will have no choice but to hire an attorney and sue him for libel and ual harment. Of course, you would win, and of course, he would lose his job and his reputation so the ball is in your court.