Why not just stir some of that and some stevia or whatnot into the already carbonated water? I realize some of the bubbles will evaporate with stirring, but if it's well carbonated, should still be reasonably fizzy. I don't like root beer at all myself, so not sure if the taste profile would be appealing in the following applications, but I use bitters (basically flavor extracts commonly used for cocktails but can be applied to many things; my favorite is mexican chocolate) in seltzer, in almond milk, added to iced coffee, yogurt, oatmeal, etc (with or without sweetener, as desired). Usually a very small amount is plenty! If you're a drinker, could probably use to make some great cocktails too.