I agree that generally most figs that have this flavor are under ripe, or at least not ripe enough to dissipate that flavor note. Some figs have a tendency to carry that melon flavor longer than others. Sometimes that melon flavor can be quite nice depending on the rest of that fig's flavors. It doesn't sound like that is what is going on for you though. Generally, every variety has the potential to make some tasty figs. You should experiment with ripeness levels of different cultivars to determine how you like "that fig". Depending on the variety, I prefer them at different stages of ripening. Some figs I leave on after they finish swelling and even after they shrink for a couple days and get wrinkly skin. Be prepared to fight wildlife if you like a particular fig at that stage though. Best of luck!