I finally got the setup working in Azure. For Sitefinity 8.x and new Azure setups here's what I had to do:
1. Create the site normally on my local machine
2. Right click and run the azure wizard but only select the first option, to prep the site for deployment (optionally you can do this manually using your documentation, but the documentation isn't clear on some of the settings for dlls and conflicts with what the wizard does)
3. Add the cloud project manually and continue with the manual steps
4. Use SQL Server Management Studio 2014 to migrate the local database to Azure. One thing to note, you have to install at least CU4 to get the right tier targets. The out of the box install uses the old Web/Business tiers and the migration will fail. CU4 has the new targets (I installed CU5 because it was available)
5. Create the deployment packages and manually add them to Azure
Thanks for your help. There are a *lot* of gaps on the documentation when doing this with the current azure portal and a lot of broken links in the Thunder wizard (for example when you click on logging in to try to deploy automatically it takes you to a broken link). I've submitted several updates to the documentation but haven't seen any changes yet.