You're going to have trouble keeping that plate in place while installing the hinge, as it will need that bolt at least loose to slide the hinge in place. I'd suggest that you drill a couple holes in the door panel where you've put the plate, but outside the depression for the hinge, and put a couple of plug welds there to hold it in place permanently. They should be covered by the door panel, so won't hurt your paint job.
If you just used the nut plate without the secondary sheet metal, you'll be depending on just the inner sheet metal skin to support the door, and it may eventually crack. I would highly recommend welding that inside sheet metal that holds the nut plate to the inner panel to give the assembly more support.
