It turns out that in our district, home-schoolers have access to the public schools' extracurricular programs. In our case, this means that Older Daughter has joined the local high school's drama club, which meets 4 afternoons a week. OD already had a friend in the club (actually, that's how we first heard about it.)
So, right off the bat, that's solved my biggest dilemma; getting OD out of the house, doing something she enjoys, with kids her age. Hooray! The depression has lifted. Now I see that we will not evolve into some horrible mother-daughter Howard Hughes phenomenon. (I have also taken on a couple of part-time jobs; one teaching math to small groups of kids, and one working on a computer program. I need to get out of the house too!)
In the meantime, Sainted Husband has been working on the academic angle; they've done some geometry, some writing, and some chemistry (not a whole lot, I'd have to admit.) SH has been reading aloud from Agatha Christie's "And Then There Were None" at night.
And that's where we are now. We have a teenager who isn't depressed, which is a huge improvement already. We could do more with academics, but the year has only just started.