Bring the rice vinegar and sugar to a boil in a saucepan until the sugar dissolves. Cook over medium heat for 10 minutes, stirring constantly. Stir in the mangoes, apricots, and ginger; cook, stirring occasionally, until the fruit is soft and beginning to break apart, about 10 more minutes. Transfer the mixture to a blender or food processor and add the honey and lime juice. Process until smooth.