I think exposing Becky won't have their desired effect though. She will just point out that all of her friends were going to vote to keep Jason (ie: vote her out) so she said what she had to say to stay in the house.
It will also solidify Becky against 6th Sense permanently.
Is keeping Shelli worth all that to anyone, other than Vanessa? The twins should be self-centred enough to see through that, even if Austin can't.