Got it to work. On the phone, I had to go to Settings, and then Data Synchronization, and make sure that contacts was synced. I guess it had been checked at one point, and it brought in email addresses, but later after I had imported all of my contacts and expected it to sync, it didn't because that box to sync contacts had been unchecked.
All is well, and this is awesome. After 10 years of manually syncing smartphones, I'm done.