Add 4 cups of the cider with all the salt and sugar to a medium-size pot and bring to a boil and cook until the salt and sugar are completely dissolved. Whisk occasionally.
Transfer the mixture to a large 5-gallon container along with the remaining amount of cider, water, onions, garlic, bay leaves, and thyme, and whisk to combine.
Preheat the smoker to 250°. Add the turkey to the smoker and cook for 4 hours to 4 ½ hours. The thigh meat should read 160° to 165° when it is finished.