I love the unique flavor of vermouth so if you want to make this closer to a classic martini, add a little and see if you like the complexity.
Martinis are served "straight up" which means not over ice. If you shake the recipe really well with ice, it will be nice and frosty when added to the cocktail glass.
About 3 medium-sized blood oranges will allow you to make 2 cocktails. If you are making a bunch, be sure to buy more!