How much shorter is the turkey's cooking time if I increase the temperature?
You can typically roast a turkey anywhere between 325 and 375, so 350 should not be an issue. AllRecipes provides cooking times for an oven set at 350. Note that a stuffed turkey will take longer to cook.  

4 1/2 hours is longer than than most references indicate for a 9 pound turkey at 325.  If you have successfully made this recipe in the oven you are planning to use, you may want to budget in an extra 30-60 minutes.  

I have found that the easiest way to keep track of the the status of the poultry is to place a leave-in meat thermometer into a thigh (but not next to the bone). The thermometer probe will stay in the meat and measure the internal temperature as it cooks.  The turkey is done when the internal temperature of the thigh reaches 160 (FDA recommends 165) and the juices are clear when slicing the thigh.