I just move the whole thing back and forth. It takes me about 5 minutes using the LATCH system that both our cars have. This includes utilizing the 3rd attachment point from the rear of the seat to the front passenger seat mounts that's included with this seat. If you only used the LATCH attachment points it would take less than 5 minutes.
its easy to move whole thing. I have never taken out just car seat and kept base in our car. I have traveled a lot with this car seat and put in different car such as taxis, mini vans etc .. Never had problem. I am not sure if they sell just base for this seat.