Place a small plate in the freezer for gel testing later. Set a water-bath canner (or deep pot with rack) to heat; keep jars and lids hot in simmering water (not boiling).
In a large nonreactive bowl, combine sugar and salt. Add about two-thirds of the strawberries and toss well. Lightly mash to release juices, then let stand 20–30 minutes, stirring once or twice.
Scrape the macerated berries and all juices into a wide, heavy pan. Set over medium heat and cook, stirring often, until the fruit is juicy and beginning to foam, 5–7 minutes. Mash to your preferred texture.
Increase heat to a lively boil (medium-high). Cook 8–10 minutes, stirring frequently and adjusting the heat to maintain a robust but controlled boil.
Stir in the remaining chopped strawberries for soft, fresh pieces. Continue boiling, stirring constantly, until the bubbles look thick and glossy and the jam reaches 219–221°F on a thermometer, 8–12 minutes more. Alternatively, spoon a little jam onto the frozen plate; after 30 seconds, it should wrinkle when nudged.
Stir in bottled lemon juice and lemon zest, then boil 2 minutes longer. Remove from heat and let the jam settle for 3 minutes; skim any persistent foam only if you like a perfectly clear top.
Working with hot, sterilized jars, ladle jam into jars leaving 1/4-inch headspace. Run a clean tool around the inside to release air bubbles and wipe rims with a vinegar-damp cloth. Apply lids and screw bands just finger-tight.
Process in a boiling water-bath canner for 10 minutes (0–1,000 ft). Turn off heat and let jars rest in the canner for 5 minutes before removing to a towel-lined surface.
Cool 12–24 hours undisturbed. Check seals, label, and store in a cool, dark place. Refrigerate any unsealed jars and use within 3–4 weeks.