I want to pass $this from my Controller to my Service Provider so I can use it with my custom class. That way, I can reference back to my controller and output the success.
That is a terrible idea, and you'll have trouble making it work anyway.
Your Filesystem class should have no knowledge of your controller class. Passing in $this and trying to get File to do your controller's work is not the way to do it. It should just do its 'file' stuff, and then return an appropriate response.
Controller
function Foo(){
if (MyFacade::Bar($input))
{
// Success
}
else
{
// Fail
}
}
Custom Class
function Bar($input){
//Some code
return true; // or false
}