Everything is possible with the right amount of work and know-how.
Idea #1 I have not seen anybody try but it seems possible. The hardest part will be creating a flexible ribbon from the LCD to the controller board that will work with the swivelly thing.
Idea #2, seems the same as #1 to me. For both of them you would need to overlay the OEM stuff onto the new screen.
To me it seems like the easiest would be to find a unit that uses standard rgb/composite feed to the stock lcd controller. Then splice those signal lines into an overlay module into the VGA signal, then run that VGA signal into the retrofitted lcd controller to be displayed on the retrofitted screen.