After looking at a pile of parts for about a month, I realized that now that I’d cleaned the frog and screws, there was no reason not to reassemble the #6 plane (other than losing a few of those parts, that is). Here’s the result:

It sure isn’t gonna win any beauty contests with that big ol’ chip missing off the front left side. More important is that all of the moving parts actually move smoothly and easily now. It’s amazing how well this stuff works when you get rid of all of the rust and apply a tiny amount of oil.
Of course, it’s not done yet. Two big things remain; first, I have to lap the sole and clean the sides. Second, the iron needs honing. Actually, it needs more than that; it needs grinding first, because the edge lists to one side. That’s sort of a big job for someone who’s never done it before, but it’s not impossible.
[edit: see the edits in this post for my current thoughts on lapping.]
Here’s the rear:

With this one in decent shape, I can move to another plane. I’ll probably do the Millers Falls #9 now. As you may recall, I already started on the lever cap from that. I’ve also cleaned the iron and chipbreaker, so given that the wood doesn’t need any special work, it won’t be long until that one is looking good, too.
At least I hope it doesn’t take too long. Other than these two planes, somehow five others have popped up that also need, uh… work.