My new Jeep has the U-Connect 8.4" computer screen. You can look up anything, from the price of gas in your area, to the best rated pizza joints. And most anything in between. It wouldn't be hard at all for them to have a page of all the different tire sizes that will clear the fender wells of a Jeep Grand Cherokee.
All you would have to do is touch the correct tire size you wish to install, then touch "APPLY", and the speedometer along with the odometer would instantly calculate the change. They could even factor in tire pressure, because it also displays the current tire pressure for each wheel in real time. I can watch my tire pressure rise as they heat up, from when I pull out of the garage on cold tires, as I drive on the freeway at 70 MPH.