Will McConnell and Boehner and Sen Grahamnesty be in charge of a Con Con? You know, these reliable conservatives.
But there is a school of thought that Article II, Section 6, would apply to a convention. Just as sitting federal officeholders cannot be presidential electors, neither can they be appointed to represent their state at a convention. But that's not 100% sure. The American Bar Association disagrees. Check my two links in that long, pedantic post I put out earlier in this thread.
Have you read any of Publius’ posts? They would have nothing to do with it. The delegates are appointed by the states and the Convention is run by the STATES.