I have not worked on a 39-40 but on my '37 the grill is installed from the backside. In other words, you have to remove the radiator or the whole front end from the truck. The grill does not install from the front. Perhaps it is the same with your truck?
It installs with screws from the front, no problem there.
The problem is that the grille is about 1/4" too wide to fit the bars inside the vertical edges of the sheetmetal on the sides of the grille.
Maybe it just needs some persuation to fit. ;-)