That looks good so let me know how you get on with the reader and software please. Maybe you can even set the right tyre diameter on these!
I have just had mine done by the dealer for the largest there that was on the JET edition with the 20" wheels and tyres, 245/50R20. That worked out at a 29.65" diameter which is 2% bigger than the rolling diameter I had with the 18" Limited wheels, 235/60R18 at 29". Speedo was already reading 3% fast so it is now spot on up to 100 kph but 1-2 kph slow at 110 for the 245/70R17 tyres which are 30.5".
https://www.wheel-size.com/size/jeep/liberty/2010/
I did notice better response straight away and even turned down my throttle unit down one bar.
He said there was a performance option that might be even better but he couldn't give me a tyre size or any more information about it but said it had to do with settings for performance type tyres and not the AT's tyres I have so didn't select it.