There are two workarounds to allow you to send as your aliases. I'll describe them both and give links on how to implement them:
1) create a POP3 account in the local Outlook that does not ever actually POP anything and uses the SMTP info for the Exchange server and the email address for the alias
2) create a distribution list with a single member (the user). Assign send as permissions to that mailbox for the user and then the user can use the FROM field. The down side is that you might be adding many different fake distribution lists for each time a user needs to send as an alias.
Both solutions are lame, but I'll be implementing option 1 from this point forward.