We’re the same way in my house. We try our best to avoid the artificial ingredients and over-processed foods. I’d rather eat/drink real sweeteners sparingly and bolus accordingly, which seems very contrary to popular opinion for diabetes. We do use low glycemic index “sugars”, though. Primarily, agave nectar and coconut sugar. For root beer, I’d sweeten with the coconut sugar because it’s almost molasses tasting, like brown sugar, which would compliment the spices well. I’d use the agave for gingerale, since it’s a little more sour tasting , like citrus, which ginger loves.
As to methods, you can either buy concentrates/flavorings, or make from scratch.
Gingerale is the easy one. If you don’t have a water carbonator, you can carbonate with yeast in just a few days. I love Alton Brown recipes, like the following one. His recipes are usually listed by weight, not volume, though. This one calls for the equivalent of 3/4 cup sugar. Agave tastes sweeter than sugar, so reduce the amount by 25% when substituting for white sugar. Since you’re looking for a less-sweet version, though, I would start with 1/4 cup of agave syrup in this recipe, and you could adjust to taste next time you make it from there.
If you do have a water carbonator, or just buy a bottle of plain soda water, just make the syrup as directed with the agave substitution, store it in the fridge, and add it to your carbonated water to taste.
Personally, my favorite is my gingerale kombucha. If you ever feel like trying the brewing process, it can be a lot of fun. I usually have kombucha, beer, Mead, and yogurt fermenting in my house all year round. When you bottle the kombucha for what’s called the secondary fermentation (this is when you trap the bubbles to make the drink fizzy), I add 14 oz Apple juice, 1/2 tsp ground ginger, and a squeeze of lemon per 2-liter bottle of kombucha. Most of the Apple juice sugar is consumed by the yeast, and I’m left with about 0.75g of carb per fluid oz. I bolus for 8g carb for an 11 oz glass of kombucha. Of course, you can easily buy ginger kombucha commercially, but it tastes disgustingly vinegary compared to homemade to comply with alcohol regulations.
I don’t have a lot of experience with root beer and wouldn’t recommend making it from scratch unless you’d enjoy it as a craft hobby, because root beer requires a LOT of ingredients. I tried for a long time to get root beer flavored kombucha, and it was just never worth the effort. I’d recommend buying an unsweetened flavor concentrate, and combine it with a simple syrup made from coconut sugar to your taste preference. (2 parts coconut sugar : 1 part water, boil on stove until the sugar dissolves completely, store in sealed jar in the fridge till needed.). You can either then carbonate naturally with the 1/8 tsp active dry yeast in a clean 2-liter bottle, like the above gingerale recipe (I’d recommend starting with 1/3 cup of the coconut simple syrup and seeing how you like that, then adjust from there)…or just combine the root beer concentrate, coconut simple syrup, and carbonated water in a glass.
That link will make a whole lot of root beer, but it’s more cost effective to buy in bulk, and the unopened bottles are long term shelf-stable. There are lots of manufactures of root beer concentrate/extract, so you might want to try a smaller volume to start with, to make sure you like it.
Note: if you plan on trying the yeast carbonating, do not bother burping the bottles like recipes always state. This is an idiot-proofing step to prevent amatuers from spraying homemade soda all over thier kitchen, but promotes vinegary over-fermentation with minimal carbonation. Just let the bottle sit at room temperature for a few days until it feels firm and just barely gives when you squeeze it, then chill very well before opening it. NEVER open a room temperature bottle done this way!! Chilling it thoroughly compresses the CO2 and reduces the pressure in the bottle. Otherwise, the bottle might erupt like a gyser when you open it. For your first attempts, I’d open the bottle slowly over the sink, just in case. You’ll figure out how easy it is really quick, though.