Cannot open database User Profile Service Application_SyncDB ... The login failed

Some of my servers were mysteriously no longer synchronizing the user profiles after some time. Upon further investigation this appeared to happen after a server reboot. Here is an error found in the Application Log with a source of Forefront Identity Manager:


.Net SqlClient Data Provider: System.Data.SqlClient.SqlException: Cannot open database "User Profile Service Application_SyncDB_35eb65afa42c4f8e9ece6a33e9348849" requested by the login. The login failed.
Login failed for user '[my user]'.
   at Microsoft.ResourceManagement.Data.Exception.DataAccessExceptionManager.ThrowException(SqlException innerException)
   at Microsoft.ResourceManagement.Data.DatabaseConnection.Open(SqlConnection connection)
   at Microsoft.ResourceManagement.Data.DatabaseConnection.Open(DataStore store)
   at Microsoft.ResourceManagement.Data.TransactionAndConnectionScope..ctor(Boolean createTransaction, IsolationLevel isolationLevel, DataStore dataStore)
   at Microsoft.ResourceManagement.Data.TransactionAndConnectionScope..ctor(Boolean createTransaction)
   at Microsoft.ResourceManagement.Data.DataAccess.RegisterService(String hostName)
   at Microsoft.ResourceManagement.Workflow.Hosting.HostActivator.RegisterService(String hostName)
   at Microsoft.ResourceManagement.Workflow.Hosting.HostActivator.Initialize()
   at Microsoft.ResourceManagement.WebServices.ResourceManagementServiceHostFactory.CreateServiceHost(String constructorString, Uri[] baseAddresses)
   at Microsoft.ResourceManagement.WindowsHostService.OnStart(String[] args)

A few seconds later in the log

Starting up database 'User Profile Service Application_SyncDB_35eb65afa42c4f8e9ece6a33e9348849'.

So, it looks like the Forefront Identity Manager Service is starting up before SQL has started the necessary databases. This appears to cause it to crash. Now that I figured out the problem, I do a search to figure out how to delay the start of the FIM Service and find this article: Troubleshoot User Profile Synchronization Service start issues (SharePoint Server 2010). Scrolling down to the bottom, there is a section titled "User Profile Synchronization service cannot start after a server restart" This suggests using the Services Manager to change the startup of the FIM services to "Delayed Start". (Note that this contradicts the Important note at the top of the article stating "Starting the FIM services manually or changing the FIM service configuration is not supported.").