Greetings,
Hayes made about 1000 coupe bodies for Chrysler Corp. in 1939, divvied up in 6 series: Imperial 8 & New Yorker (125" WB), Royal 6 and Royal Windsor 6 (119" WB); DeSoto Custom (122.5" WB); Dodge Luxury Liner Deluxe (117" WB).
Here's a suggestion. Since the bodies are all the same, measure the Dodge body in the museum, and find a '39 Chrysler coupe for the front clip and rear fenders. The extra wheelbase length is from the cowl forward. As I recall, the trunklid has a distinctive ridge right down the middle and through the split backlight.
Also, I know I've seen a feature on the '39 Imperial 8 Club Coupe in the last 5-6 years, maybe in CARS & PARTS. It was a cream color and I remember coveting it for its extreme rarity.
Can't wait to see the model!
Tom Gibson