Hello, @fredrikaa,
I have never heard radiometric dating methods related to GPS satellite systems. I would like to see your source for that connection?
I do not have a problem with a very old universe. However, time flow is not a constant everywhere. If you would kindly have a look at my previous article in this series, and investigate the work of Dr. Russell Humphreys, you can see considerably more information about how the Earth can simultaneously be very young while the universe is very old.
Also, while it has been many years since I looked at these particular details, I do not believe that the geological layering is particularly consistent, and so I would also welcome specific reference data in that regard.
Thank you for stopping by, and please feel free to add some specific references or data to your comment if you would like to. I will gladly have a look! :D