I've been combing through the Powershell commands trying to figure out how to take my currently deployed Website/SQL Database/Storage account and move them into their own Resource Group.
Is it possible to move Azure "Resources" between Resource Groups? Or do I always have to create new Resources and migrate the data/code into those new Resources?
It is now possible to do what you want in PowerShell, I believe. This blog post provides an overview of how to do it: http://blog.kloud.com.au/2015/03/24/moving-resources-between-azure-resource-groups/
The features are available as of Azure PowerShell cmdlets v0.8.15.1, I believe.