Cutting three-quarters of an inch off the bottom of the bookcases fixed the height problem. But as I was installing them I noticed something. The first shelf went in and one side went further back than the other. I did some exploratory pushing and things didn't even out. So I kept on keeping on, which is often what I do when confused during projects.
The next bookshelf had the same problem, but the amount of space covered kept getting bigger. "Maybe this back part isn't square?" I mused. Matt turned around, took one look and said, "nope. There aren't two 90 degree angles on this end.
It took a while for my head to adjust, but these rulers prove it. This end of the counter doesn't even measure 12 inches. If you look at the other end, there is a silver 12-inch ruler that doesn't reach all the way across. I've been living with a trapezoid and never noticed!
Here you can see how my trapezoid shrinks. I'm pretty sure this was intentional. Maybe to make the transition from great room to hallway/kitchen less abrupt.