I don't think those specific ingredients actually "Sweeten" tomatoes. This may be just a folklore.
There are varieties of tomatoes that have sweet flavor/higher in sugar content, some that are higher in acid afterburn, and ones that have NO acidity. There are varieties that have what can only be described as umami. Some people say some varieties are salty. I think these are the flavor qualities that creates sensation of added sweetness. Tomatoes that are only sweet but have no other flavors to me lack the necessary finish. DH and I have looked at each other and SAID it starts out sweet and good, but WHERE'S THE REST!?
So you need to learn what kind of tomato flavor profile is to your liking, and grow those varieties -- if not this year, then next year. In the mean time, to work with what you have and improve their flavors ---
When tomatoes get too much water near to harvesting, whether by irrigation or rain, the flavors naturally get diluted.
Healthy tomatoes growing in rich organic soil with balanced diverse nutrients and minerals will develop their genetically programmed flavors to the fullest. So if you soil is lacking in any of the nutrients and minerals represented by the ingredients you listed, the tomatoes COULD naturally become better flavored if you were to supply them in time for the plants to absorb them.
I would say eggshells could be dried and ground up into a powder, then you won't have to worry about digging them in. They will break down quickly or quickest method when smallest size.
Epsom Salts contain Magnesium and Sulfur, which are vital in small/tiny amounts -- these are part of micro-nutrients needed by the tomatoes. Typical recipe is 1Tbs per gallon and 1 tsp per quart. But I would dilute that even more when it's hot and soil tends to dry quickly, since evaporation would concentrate the solution.
Liquid solutions can be delivered deeply into the soil by pounding a pointed PVC pipe in the ground and pouring your liquid in it. (You could even add your eggshell powder). This shouldn't be done right by the stem where the branched roots originate -- severing those could cause significant root system disruption -- but out where the feeder roots are, which typically for all plants is under the very TIP of the leaves. This means you would do this in several quadrants around the tomato for even supply.
Some liquid solutions can also be foliar fed. This means the plants will absorb them through the pores in their leaves. But conditions need be just right and the solution need to be applied as micro-fine mist. Too concentrated or applied at the wrong time of the day -- sunny, windy, etc. -- can spell disaster and burn the leaves and fruits. I would not try this until you are familiar with the process.
Baking Soda -- Sodium Bicarbonate -- I don't see how any of these molecules need to be supplied as a micro-nutrient, but Baking Soda will raise pH -- make more alkaline, which process is *called* "sweeter" and adding lime or other alkalining agent to amend soil is described as "sweetening" the soil. Only way this would benefit tomatoes is if you soil is ultra excessively acidic, since tomatoes prefer soil pH that is slightly more acidic than completely neutral.
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