Seems to me this course demands the heroine both to press charges and to become a witness, and I'm not sure how much that can be kept quiet. It also doesn't stop the blackmailers from talking to the press and smearing her name, since they're already busted -- what have they got to lose?
At the end of the day, there really are only three options to get out of blackmail:
1) Make it impossible: remove all evidence or kill the blackmailers
2) Make it unwise: counter-blackmail, some threat or another
3) Make it powerless: own up to the truth proudly and find a new job....
It might actually make for an interesting story (with some emotional/psychological depth) to have a caring colleague coax her into trusting him, then helping her make the big step for #3. And of course, helping her deal with the consequences -- we live for the "comfort after the hurt", after all