I was hung up on a label, but the more I think about it, the more I like neo-reactionary, for the reasons Lawrence Auster gives in a comment at Mangan's:
"Neo-reactionary"--that's clever. The neo-reactionary is not an old-fashioned, hardline, darkly pessimistic reactionary, like de Maistre, but a modern, enlightened, cool reactionary. To paraphrase Irving Kristol on the purpose of neoconservatism, one could say that the historical task and political purpose of neo-reaction would seem to be this: to convert American reactionaries, against their will, into a new kind of reactionary capable of living in a modern democracy.There's also a post from Arnold Kling, discussing Codevilla and referencing Moldbug in passing.
The only change I would make is to elide the hyphen. Neoliberals and Neoconservatives don't need them any more, and I thnk google's search syntax treats a hyphen as a space. Neoreactionary will bring back only neoreactionaries.