You are making this way more complicated than it needs to be. This is such basic carpentry that I was probably 10 years old when I did it the first time with no power tools and only very basic hand tools. You take a piece of wood, any wood but pine without knots is easier to work, sand or plane one side and one edge, flat and smooth. You saw or plane it to slightly wider than the mortise, saw off about a quarter inch thickness and saw to length, glue into the mortise and when set, plane to flush with the door edge and side. If needed touch up with wood filler. Done.