I think the easiest way to do it would be to script out all of the stored procedures that do cross-database communication, drop them, generate the bacpacs, import the bacpacs, recreate the stored procedures from the scripts you created.
Although, are you sure you can import a SQL Server 2008 bacpac to an Azure SQL Server? I would probably double check the docs as you MAY (likely will) need to upgrade to a supported version of SQL before doing the import. I am fairly confident that 2008 won't be able to migrate to Azure without doing an upgrade first.
As far as I am aware, you cannot create a bacpac that contains multiple databases.
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!
I recommend you NEVER run "random code" you found online on any system you care about UNLESS you understand and can verify the code OR you don't care if the code trashes your system.