Arrange racks in the upper and lower thirds of the oven and preheat to 325°F (163°C). Line two large rimmed baking sheets with parchment paper, keeping the paper flat so the macaroons sit level. Avoid greasing the parchment because added fat can encourage spreading. Check that the mixing bowl and whisk for the egg whites are completely clean and grease-free, then separate the room-temperature whites without allowing any yolk into the bowl.
Place the loosened sweetened shredded coconut in a large mixing bowl. In a separate cup, stir the condensed milk, vanilla, and half of the salt until smooth, then scrape this mixture over the coconut. Fold with a flexible spatula until every strand looks evenly moistened and no dry pockets remain. Let the mixture stand at room temperature for 10 minutes; it should become cohesive and hold together when squeezed, but it will still feel thick and sticky.
Add the cream of tartar and remaining salt to the egg whites. Using an electric mixer, beat on medium speed until foamy, then increase to medium-high and continue for 2 to 3 minutes. Stop when the whites form glossy medium-stiff peaks that stand with slightly curved tips. Fold one-third of the foam into the coconut mixture to loosen it, then gently fold in the remainder in two additions until no white streaks remain and the mixture feels lighter.
Using a 2-tablespoon cookie scoop and the digital scale, portion the mixture into 24 mounds weighing about 35 grams each. Pack each scoop firmly enough to create a stable base, then place the macaroons at least 1 1/2 inches apart on the prepared baking sheets. With slightly damp fingertips, press any loose sides inward and pinch a few strands upward for craggy tops. Do not leave long, wispy pieces exposed because they can scorch before the centers set.
Bake for 20 to 24 minutes, rotating the pans from front to back and switching their rack positions after 12 minutes. The macaroons are done when the bases and outer ridges are deep golden brown, the tops feel dry, and the centers resist gentle pressure without feeling liquid or collapsing. An instant-read thermometer inserted into a center should register at least 160°F (71°C). Cool on the pans for 10 minutes, then transfer carefully to a wire rack and cool for 25 minutes before serving.