Okay -- it isn't by any means perfect, but so far it's the best solution I've come up with.
The only thing I miss, in moving from LiveJournal to Dreamwidth, is the native support for cross-posting from here to FB. So for the past couple of months I've been exploring alternatives. The one I've been using was dlvr.it, as described here -- that's adequate, and makes it fairly easy to post links on FB that point to your posts here.
But the thing is, I don't love that, because not many people actually click through those links. And while I may not love FB, I do have a lot more friends there than on Dreamwidth, so I'd like to be able to actually cross-post, not just link.
For a while, I had thought that the answer was Zapier, and I put in a lot of work getting a true cross-post solution working there. But Zapier has one critical flaw: the approach I'm using for cross-posting requires a feature that only exists in their paid version, and Zapier is insanely expensive. (Like, $20/month.) It's just not worth that kind of money. (Yes, I talked to them about it; they brushed me off and refused to even contemplate a more reasonably-priced tier.) So I gave up and went back to dlvr.it.
So I've spent a little time in the workday cracks today taking the solution I'd built for Zapier and adjusting it for IFTTT. The experience with IFTTT is a bit different from that of Zapier -- a bit less powerful (in particular, their RSS reader doesn't pick up your DW tags, which Zapier did), but with a much better built-in IDE.
I think that's now working adequately -- it's not The One True Solution, but it mostly works. I've published it as a public Applet on IFTTT; feel free to pick it up and use it. You give it the URL of your Dreamwidth RSS feed, and you need to connect Facebook to IFTTT; once you have that, it should, in theory, quietly check your RSS feed every 15 minutes or so, and cross-post new entries to your Facebook wall. It takes each DW post, translates it into something that looks okay on Facebook (basically, it back-translates the HTML to something vaguely like Markdown), and includes the link to the original DW post at the bottom.
Please pass word on to anybody who might care, and tell me about problems. (Hopefully, I can fix any problems -- once I published, IFTTT gave me dire warnings that I could no longer alter my triggers or actions; hopefully I can still edit the critical filter in the middle.)