Several references online quote Chris Hannah as saying his preferred rum for this is Plantation OFTD, which would make for quite a different drink than with the Cruzan. Furthermore, he calls for Amer Picon, but says that Averna makes a good substitute. To confuse it more, some references have the amounts for Chartreuse and Picon/Averna flipped.
A few of Chris Hannah's recipe have drifted over the years such as the Rebennack. This would not have been invented with OFTD since it had not been invented. This is the one I sourced from Under the Table: A Dorothy Parker Cocktail Guide and wrote about here: https://cocktailvirgin.blogspot.com/2015/06/bywater-cocktail.html
1 3/4 oz Aged Rum, 3/4 oz Picon, 1/2 oz Green Chartreuse, 1 tsp Falernum, 2 dash Peychaud's Bitters, 2 dash Orange Bitters. Stir with ice and strain into a cocktail glass. Garnish with a cherry.