The concept of a "dry Martinez" is faintly ridiculous, since the Martinez is essentially the older, sweeter cousin to today's Martini. For bonus irony points, this isn't even really all that dry, though it is a fairly-dry rendition of the Martinez formula. It is brand-specific (that's the "double" part of the name) and I apologize for that, but this Dry Rye stuff really does deserve hunting down.
2 oz St. George Dry Rye gin
1/2 oz dry vermouth (Dolin here)
1/4 oz sweet vermouth (Dolin again, any decent vermouth would do fine)
1/4 oz maraschino (do I even need to specify Luxardo at this point?)
1 dash simple syrup (not exactly "dry" but helps with the balance)
1 dash Angostura bitters
1 dash Bittercube Cherry Bark Vanilla bitters (an astonishing combo with the Luxardo)
Stir and strain into a chilled cocktail glass; squeeze an orange twist over the top if available and discard, then garnish with a lemon twist. That's what I did, anyway; a twist of either citrus will do just fine as garnish.