Wooden bucks to form the grill work into accurate contours might be a simpler process and gets you around having to use special equipment. It requires carving a block of wood able to fit snuggly up against and inside the shell openings. Holes for grill alignment on the buck will aid greatly in accuracy and allow soldering the entire assembly at once. If it's possible to fabricate both grills as one assembly then the project becomes simpler still.
The styling resemblance to the Budd produced Pioneer Zephyr is obvious and begs the question, did both company's work on this unique pair?I