Merkuri
Explorer
This sort of cross chatter is very common for my group, so I don't see any problem with a contrived version of same for the OP if it works out for him. I also don't see it as belittling or demeaning the player in question either. In fact (putting on pop psychology hat) I see it as a positive reinforcement to do the right thing even if it results in bad consequences.
My complaint about that option is that, depending on how the group is doing it, it may become very obvious that the cheating player is getting all of the attention when she rolls, which may end up being seen by her as a not-so-subtle way to punish her for cheating. She'll probably realize very quickly that everybody knows she's cheating and that you've talked about it behind her back to come up with this "yell out her rolls" plan - and nobody likes finding out that they've been talked about behind their backs. (Now, I'm not saying this is definitely how it'll play out, just that it's very possible.)
If you're trying to eliminate drama the best (IMO) way to do it is to implement a rule or behavior that affects everyone, not just the cheating player. If you're going to have people calling out rolls for the cheater, encourage them to call out the rolls for other players as well. Doing things that affect everyone will make the cheater feel less like she's being singled out and talked about behind her back.