Ginger Beer Carbonation in Glass Bottles

I have several liter glass bottles with swing tops that I want to brew Ginger Beer in using the following recipe; however, this recipe calls for so much sugar that it will cause the bottles to explode unless I refrigerate them. I had planned on using just a little bit of sugar to carbonate the bottles and sweetening it with Xylitol or some other artificial sweetener.

How much sugar or what Specific Gravity should my mixture be so it will carbonate without exploding?

Ginger Ale
Makes about 8 cups 
(enough to fill a 2-liter plastic soda bottle)

2-inch piece fresh gingerroot
1 cup water, plus more to fill the bottles
9 tablespoons / 4 ounces white granulated sugar, plus more if needed
1/8 teaspoon salt
5 tablespoons freshly squeezed lemon juice (from 2 to 3 lemons), plus more if needed
1/8 teaspoon dry champagne yeast

Adequate carbonation really only drops gravity by a couple of points. Whatever your gravity comes to be without the sugar, add sugar in to bump it up so that the calculation for ABV comes out to 0.4-0.6% and that should get you where you need to be. Sweeten to taste with splenda, stevia, or whatever else you have on hand that's non fermentable.

Can't you pasteurize bottles when desired carb level is achieved?