So the frame is clean: no more grease at all. That concentrated Dawn is powerful stuff! Yike. There's more rust under all that dirt than I thought. The tip of the metal nail file ain't going to cut it. Off to get new tires put on my car, so I can walk over to the store and get some rust remover and clear nail polish while they fix up the Honda. I hope it works, as I'm at a bit of a loss otherwise. The rust is everywhere, in little scratches and big patches and more rhyming things. I'd have to scrape off half the paint to get it all, I think! <insert more hyperbole here> The top and bottom of the headset (?) is rusted and pitted very badly, and since it's attached to the painted part, I can't really do much with it if the rust remover doesn't do the trick. I'll keep you posted.
I did polish up a wee area with some Mother's scratch remover (that's what I have, not the Meguire's), and you guys were right: it makes a big difference. The minor stuff is all gone and the paint is noticably more glossy there. Progressing nicely, I think, if I can get the darn rust off.