How to sandbox and run programs that require administrator privileges on limited-user PC?

You could use VMWare to create and boot up an operating system that does give you administrative permissions. It would solve all of your requirements in that it would be sandboxed and completely separate from your host OS, and you would be able to run programs, save to virtual disk, etc, all without having to change permissions on the host OS.

Spoon.net - create the app on another computer with spoon, and then it will run it on anything, if you can build it in spoon successfully. no admin rights needed.