Wow. I am stumped on this one. I would certainly boil it for 10 minutes to sanitize it. Your idea of subtracting the total weight of sugar in there makes sense.
How about this - Take a proportional amount of beer to fig juice and play with it till it tastes OK. Say 50ml of beer and then 5 ml of juice. Taste, swish and see how it tastes and change the ratio till it tastes right. I am sure it will change in taste as it ferments again to carb the bottle but at least you will have some idea of how much it will impart.
Another thing too is what kind of sugar is in fig juice and is it readily fermentable by the yeast? I just don't know.
Let us know how it comes out!
Primary - Dunkleweizen, Hefeweizen, Marzen/Festbier
Secondary - THIS SPACE LEFT INTENTIONALLY BLANK
Conditioning - Oaked Whiskey Imperial Stout
On Tap - NITRO Dragon's Milk Clone (Drago's Sweat), Cafe Con Leche Stout