Bring a large pot of water to a boil. While it heats, cut peaches in half and remove pits. Fill a large bowl 2/3 of the way up with cold water (the cold water stops the cooking and cools the peaches down enough for you to peel them).
Working in batches, blanch the peach halves for 1 minute. Use a slotted spoon to transfer to the bowl of cold water. When cool enough to touch, slip off the skins.
Finely chop the peaches. Measure 4 1/2 cups. Place the peaches in a 6- to 8-quart nonreactive pot. Using a potato masher, smash the peaches. Stir in lemon zest, lemon juice, and cinnamon.
In a small bowl stir together 1/4 cup of the sugar and the pectin. Stir pectin mixture into peach mixture. Bring mixture to full rolling boil over high heat, stirring constantly. Stir in remaining sugar. Return to full rolling boil and boil exactly 1 minute, stirring constantly. Remove from heat. Skim off any foam.
Ladle jam into 5 hot, sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe rims, apply lids and rings and process in a boiling water canner for 10 minutes. Remove jars from canner and let cool on a folded kitchen towel or wire rack.