Hi Mscrutts,
Since DirSync is not available, I suggest you perform a Cutover Migration. The migration service provisions new mailboxes in your cloud-based organization automatically. It creates a cloud-based mailbox for each user account in your on-premises Exchange organization. After the migration is completed, assign licenses to the new mailboxes. Then, the users can use the Office 365 mailboxes. For detailed steps, you can refer to the following help article:
Migrate All Mailboxes to the Cloud with a Cutover Exchange Migration
http://help.outlook.com/en-us/140/ms.exch.ecp.emailmigrationwizardexchangelearnmore.aspx
Thanks,
Mindy Pan