MakerBot is printing again, but I'm not going to rescind my posts of frustration just yet.
It turns out the problem was that my threaded Z rods were really bent. Most MakerBot rods apparently are. This was causing a wobble, which was causing a variance in the tension of my Z belt.
Solution : rotate each Z rod such that its wobble is in phase with the other. Then, when they wobble about, they will all move in the same direction at the same time. This causes less variance in the tension on the Z belt, so you can actually adjust it to turn reliably.