I removed the grille and radiator from my (Avatar) '35 fordor sedan, about 12 years ago, when I replaced the original engine with another '35 engine that had just been totally rebuilt. I decided to remove the grille first and then the radiator. I can still remember what a pita it was to get the grille mounting hardware out first, and then remove the radiator. Then putting it back together in the reverse order was another pita.
Several years later it became necessary to remove the radiator again, but this time I tried a different approach. I removed the hood, hood/grille ornament, radiator support rods, all the fasteners holding the radiator in place. The four rad hoses, the cooling fan, generator, water pumps, outer distributor caps, plug wires and wire loom conduit as an assembly, and finally the distributor.
Then with extreme care, I Iifted the top part of the grille that goes over the top radiator tank, and tilted the top of the radiator back towards the engine, which freed the radiator, and allow it to be carefully lifted up and out of the engine compartment.
This may sound complicated and like a lot of extra work, but overall, this was easier for me than removing the grille first, and then removing the radiator, and then putting it back together in reverse order.