Place two small plates in the freezer to chill. If storing on the shelf, set a canning rack in a large pot, add jars, cover with water by 1 inch, and bring to a simmer. Turn off heat and cover to keep jars hot.
Peel the peaches with a paring knife or blanch briefly in boiling water. Halve, pit, and chop into 1/2-inch pieces, tossing with lemon juice as you go. You should have about 6 cups of prepped peaches.
Transfer peaches and lemon juice to a heavy-bottomed pot. Crush with a potato masher to desired texture. Stir in the full box of powdered pectin until dissolved, then add the butter.
Set the pot over high heat and bring to a full rolling boil that keeps bubbling even when stirred. Stir frequently to prevent scorching. Have the measured sugar ready beside the stove.
Pour in all 4 cups of sugar at once, stirring constantly. Return to a full rolling boil that can't be stirred down and boil hard for exactly 1 minute, stirring the whole time. If using a thermometer, cook until 217 to 220°F (103 to 104°C).
Remove from heat. Spoon a teaspoon of jam onto a chilled plate and freeze for 1 to 2 minutes. Drag your finger through; it's ready when it leaves a distinct trail that doesn't flood back. If runny, boil 1 to 3 more minutes and test again.
Skim any foam off the surface. Using a funnel and ladle, fill hot jars leaving 1/4 inch headspace. Wipe rims clean, set lids on, and screw bands on fingertip-tight.
For shelf storage, process filled jars in a boiling water bath for 10 minutes (adjust for altitude above 1,000 feet). Remove with a jar lifter and let sit undisturbed for 12 to 24 hours. For refrigerator jam, skip processing and refrigerate once cool.