Alex,
The short answer: You can't
The long answer: Is God calling the christian to hang in there? Is God trying to achieve something else? Is there any form of abuse taking place that one is being called to carefully and analytically document (without emotion clouding the picture) and then report through an established process? Are there others that are standing with the christian and advising them to stay or leave?
Usually false teaching will have other sins manifest but is it false teaching or just a different (genuine) interpretation of scripture that is not heretical?
Are there other ways to achieve your ends? What is the purpose of being on the committee? Are you called to wipe the dust off your feet and leave?
When I was a hot-head that knew everything I got into a very big spat within a church. I was right and I knew I was right. I confronted the others. Unfortunately, even though I was right and something happened that could have been avoided, I acted wrongly. God had something bigger that he was sovereignly allowing and I forgot that "They will know you are christians by your love for one another".
I have since heard from a loving christian who is just as much a sinner as I am what it is like when I am on full attack mode. Honesty from a friend is a beautiful thing. He was on "the other side" of the issue I mention above. He has helped me understand that public attack is not helpful but private expression of concern can achieve much (even though people will not always see the truth).
In terms of GAFCON etc. I find it interesting that high profile Anglicans are not leaving the Communion until they are forced (eg. J I Packer). We have recently been called back into the Anglican Communion and it is certainly an interesting journey at the moment.
Phil Weickhardt
Kalgoorlie, WA