Place the egg yolks in a bowl. In a medium saucepan, combine both sugars, salt, cream and milk, and cook over medium-high heat until the mixture begins to steam, 3 to 5 minutes. Slowly pour half of the warm liquid into the egg yolks, whisking the whole time to prevent the yolks from curdling. Whisk the yolk mixture into the remaining cream mixture. Cook the mixture over medium heat, stirring constantly using a heatproof spatula or wooden spoon, until the mixture thickens and you can see a void when you run your finger across the back of the spoon, 3 to 5 minutes.
Strain the custard into a medium bowl set over a large bowl of ice. Let cool completely while stirring occasionally. Stir the rum into the cooled custard base and process in an ice cream maker according to the manufacturer's directions. Transfer to an airtight container and cover. Freeze until firm, at least 4 hours.
To make the floats, spoon 2 scoops of ice cream into each glass. Pour a shot of dark rum over the ice cream, top off with ginger beer and garnish with the lime wheels.