D’OH! System halt.
My web host has done more reconfiguring. From this point forward, the server will choke and refuse to parse any world-writable script it sees. Which is fine and sensible; however, Movable Type as I have it set up likes to output world-writable files, and I am not going to run around manually changing permissions on hundreds of archive entries.
I wish they’d tell me before doing things like this.
If you’ve encountered a similar problem (maybe you’re just more security-conscious than I?) or you have a deep understanding of MT’s file system arrangements for whatever other reason, please please email me. DO NOT attempt to leave a comment here, it will explode my tenuous band-aid.
Update: Things are sort of mostly working again, I think, after putting MT into a secure little wrapper. And breaking some stuff along the way, and fixing it again.