It was the two largest cogs, and as I said, after I messed with it some, it will shift into all but the smallest cog, but not smoothly. It's definitely hanging up and definitely not the adjustment. No obvious kinks, no visible corrosion, nothing unusual-looking to take a picture of. Nothing that looks the slightest bit different from the way it looked two weeks ago when everything was fine. It's just hanging up inside somewhere.

I'll try the procedure you recommended for lubing the end of the cable on the down tube - but I really think the problem is "north" of there. As I said, nothing visible.