Rothbard's contemporaneous newsletter says that your "gang of four" of the 7 Radical Caucus Central Committee members made a last-minute "stab in the back" (allegedly in exchange for promises of campaign jobs), and took at most only 30 radical votes over to the Cato candidate you guys had been heartily attacking up until then. It seems misleading to suggest that a majority of radicals backed the Cato candidate at the 1983 convention.
The Boaz essay above gives a taste for the unfairness of the radical criticism of the moderates, but to appreciate the outright viciousness, you have to read Rothbard's newsletters themselves. They're simply chilling.