I figured it out. We'd placed the springs and ball bearings correctly under the burr (first the springs go in, then the balls) but we hadn't aligned the top plastic piece above the burr with the bottom one that the burr sits on. There is a tiny notch that needs to fit together, and you can't feel it by spinning them together because they don't touch until everything is screwed and tightened. You have to look to make sure they're aligned before you start screwing everything back together. Hope this helps someone.
This video and the comment thread helped us figure it out: https://youtu.be/lC2eRr5kbvY