If the table is 4ft square how much movement do you need? If it is 4ft each side of the centre that means you are having to have a 12ft square area for this device. That is enormous. I have been looking at x-y tables for the last year and there is nothing remotely at this size available. I am not sure what you expect to pay but something like this is probably going to cost at least $5000 to have made for you.
Stepping motors are common because they are cheap and easy. With DC motors you have the problem of integrating the position sensing with the motors. This gets very computationally heavy and is known as "servo systems". It is all about defining step response time and calculating critical damping, or under damping feedback functions depending on how you want it to move. It's the sort of thing people used to do with analogue computers in the 60s. You can do it with digital computers but it involves integration and differentiation.
I don't think GPS would update fast enough to allow you to use it. Are you sure you have to move the table and not say a pen or extruder over the surface?