It looks like my migration may work after all, although I haven't worked out the nits yet.
As I recently mused, what I've done is export all the entries into the one large file the system produces. Then I went into Homesite and split it up into 100-post pieces. Then I FTP'd each piece one at a time to the /import directory on the new system, running the import function each time, and then when they were all there I rebuilt the site (rebuilds on the new ISP are MUCH quicker than on the old). In theory I could have used the MT admin interface to upload the files, but there's apparently a bug in it because despite saying that the import was successful, it obviously hadn't worked.
Meanwhile I'd manually scrolled through the pages of each individual entry to figure out which IDs were missing. This wasn't as tedious as you might expect... Then before I uploaded the export files I inserted dummy posts in the gaps. This, too, wasn't quite as tedious as you might expect, and it did give me a chance to fix some of the bizarre punctuation that had gotten into my posts during the last upgrade. I don't know if I caught all of it, but I caught a lot.
But I'm not out of the woods yet. For one, I still may have gotten out of sequence. All it takes is one extra or too few dummy posts and the whole thing will need to be redone. And to redo it I think I'll have to reinstall MT all over again. Plus I noticed that there are problems with the site templates over on the new system, so that will take some troubleshooting (e.g., the front page didn't rebuild to display any content).
So I think I will semi-lift my content freeze while I work this out. Comments will remain off because I can't limit them to recent entries (in theory there's a way to, but that's not what I want to devote my energies to figuring out right now) but I may keep posting. I'll just export and import the new entries when I've got this all ready to go.