Jason,
I went back through and complete the same steps as before, and this time the email address alias successfully added to the user. Not sure what happened the first time around. I did have to add both SMTP:primary@domain.com as well as smtp:alias@domain.com to the proxyAddresses attribute, because only adding the smtp:alias@domain.com caused the primary email address to change.
For others who might find it helpful, here's a recap of the steps:
1. ADSIEdit - proxyAddresses attribute for all users is empty. Add SMTP:primary@domain.com and smtp:alias@domain.com.
2. Force DirSync
3. Wait for changes to appear in Office 365 portal
Thanks,
Zach