Looking at my grille clips, they are a bit different than yours. The reason is because the grille inserts are different. The earlier cars used a grill that had smaller squares and was basically flat on the backside (similar to my Ponton grille). My '68 W111 grille insert has reinforcing ribs side to side on the back side. So my clips actually fit on these ribs and have a narrow slot for that. It looks like your clips have a tab that fit into the square hole.
Joe's idea sounds good and I just remember it wasn't as easy as it looked.