Sterilize jars, lids and rings. Add about two-thirds of an inch of water to each jar, place the jars into the water-bath canner and cover them over with enough water to submerge them.
Place the canner on the stovetop over medium-high heat to sterilize while you prepare the jam. Place lids in a small saucepan with water and bring to a boil on medium-high heat. Allow to simmer while you prepare the jam. The rings don't even need to be sterilized; simply let them sit aside.
Process the cranberries and the orange, cut up, in a blender. Add the strawberries, orange zest, and spices and blend for just a second or two to combine everything together. You're aiming for chunky; you don't want this mixture to be a puree.
Bring the fruit mixture and water to a boil in a 5-quart stockpot, stirring constantly. Stir in fruit pectin and ½ teaspoon of butter to reduce foaming. Bring the mixture to a full rolling boil over high heat, continuing to stir.
When the mixture reaches a boil, add sugar, bring the mixture back to a full rolling boil, and boil for exactly 1 minute. Skim off any foam with a metal spoon.
Pack hot jam immediately into sterilized jars, leaving ¼ inch of headspace. Wipe the rims with a clean, damp cloth and top with hot lids and screw on rings until finger tight. Return the jars to the water-bath canner.
Close the canner and bring to a rolling boil. Process the jars for 10 minutes. Turn off heat, remove the lid, and let the jars rest in the canner for 5 minutes. Remove the jars carefully from the canner to a towel-covered countertop and let sit undisturbed for 24 hours.
Check that the jars are sealed. If any of the jars did not seal, refrigerate the jars and consume within 2 weeks.