I made the Sweet & Savory Tomato Jam from the Food52 Cookbook. It was DELICIOUS. Although after reading on-line comments and using 1/3 of a cup less sugar, I still found the jam very sweet. The recipe instructs to heat up all the ingredients (including all of the sugar) at the beginning of cooking. My question is whether it is necessary to add ALL the sugar at the beginning. Would the recipe still work if one cooked say 1/3 or 1/2 of the sugar at the beginning and then added more sugar after an hour or so cooking after tasting to adjust for personal preference (similar to adding salt closer to the end to adjust for tastes) or is it important that the sugar cooks down the entire time?