How to mount pcb with IEC320-C14 power entry connector inside enclosure
I would find some plastic standoffs with a length equal to the distance between the board and the faceplate. Drill holes in the four corners of the board that will allow you to mount one standoff at each corner. Screw the plug to the faceplate (as in your first approach) then solder the board to the plug. Drill holes through the faceplate that will line up with the holes in the four corners of the board. Put a standoff at each of the four corners, and screw into it from the back side of the board and the front side of the faceplate, so the board is securely mounted to the faceplate. Now you can attach the rest of the enclosure to the faceplate.

Since you are dealing with lethal voltages I recommend plastic standoffs, but metal ones could be used at lower voltages or if you are careful to physically isolate them from dangerous voltages.