We are looking at using an 18-20 pound turkey. How would you recommend changing the cook time and temperature for the larger turkey?

You can keep the oven temperatures the same, but you'll need to cook your turkey longer once you turn the heat down to 325. Spatchcocked birds tend to cook a bit more quickly than a standard turkey, so start by adding another 15 minutes/pound to the cooking time (at 325). If you make an 18 pound turkey, it will likely need about 3 hours once you turn the heat down. But because all turkeys and ovens are special flowers, you should absolutely rely on your meat thermometer to make sure your turkey is done, and start checking it 30 to 45 minutes early to avoid overcooking. It won't hurt the turkey to sit at room temperature for a few extra minutes, so better to start cooking earlier than have to deal with hungry guests!