Process 1/4 cup sugar and lemon, lime, and in a food processor until sugar is yellow and zest is broken down, about 15 seconds, scraping down bowl if necessary.
Transfer lemon sugar to a small bowl; stir in the remaining 1 cup sugar
In a standing mixer fitted with the paddle attachment, beat cream cheese on low to break up and soften slightly about 5 seconds
With the machine running, add sugar mixture in a slow, steady stream; increase speed to medium and continue to beat until mixture is creamy and smooth, about 3 minutes, scraping down the bowl with a rubber spatula as needed.
Reduce speed to medium-low and add eggs 2 at a time; beat until incorporated, about 30 seconds, scraping sides and bottom of bowl well after each addition.
Add lemon juice, lime juice, hibiscus vinegar, vanilla, and salt and mix until just incorporated about 5 seconds.
Add heavy cream and mix until just incorporated, about 5 seconds longer. Give batter final scrape, stir with a rubber spatula, and pour into prepared springform pan.
Bake until the center jiggles slightly, sides just start to puff, the surface is no longer shiny, and an instant-read thermometer inserted in the center of cake registers 150 degrees, 55 to 60 minutes.
Turn off the oven and prop open the oven door with a potholder or wooden spoon handle; allow the cake to cool in a water bath in the oven for 1 hour.