Combine the first 13 ingredients in a medium-sized pot. Bring to a boil, uncovered, then reduce the heat, cover and simmer for 30 minutes.
Remove from the heat and let steep, covered, for an additional 30 minutes. Using a fine-mesh sieve, strain the mixture into a quart-sized measuring cup.
If time allows, let the mixture sit overnight in the refrigerator to let sediment settle to the bottom.
Using basket-shaped coffee filters (try securing the filter over a small, round, fine-mesh strainer and placing the strainer over a vessel that will hold it upright), strain the mixture again, in ½-cup increments, with each batch using a new coffee filter (this will take up to two hours, but the process doesn’t need to be carefully or cautiously monitored, just checked on now and again).
Measure the volume of the completely strained concentrate.
For every cup of strained concentrate, add ½ cup sugar (or ¼ cup agave) and ½ t. citric acid.
Stir to incorporate and dissolve any sugar granules.
Pour the syrup into an airtight jar and refrigerate where it will keep for several months if using sugar, or several weeks if using agave or other sweeteners.
To make tonic sodas, use 4 parts carbonated water to 1 part syrup—taking care not to shake the bottle of syrup when pouring as it will stir up any cinchona bark residue settled at the bottom of the jar.