okay, got into this post a bit late, but this is what I would suggest (I don't know if it would work):
I'd make an apple wine with somewhat less sugar, and at the point where it's most frothy in fermentation, I'd raise the surrounding temperature and add 1 cup of melon juice (let's say canteloupe) at a time with a cup of sugar. Keep good track of how much you use, but I would say for a 1 gallon batch, 2 pounds of sugar total. Then, when it's really going along, do it again with the melons and the sugar.
My reasoning is this: you want vigorous and fast fermentation because melon seems to spoil on everyone. So, if you reintroduce sugar as well as the melon, AND your keeping your temperature higher (for a faster fermentation),you might be lucky. Personally, I'd do melon juice instead of fruit, so you don't have to worry about the pulp when you add it.
Make sure your SG is at least 1.080 or so, so if it does finish quickly, it won't spoil because of too low alcohol content.
Just my thoughts - I never did something like that before, but it might be worth a try.