Just wondering if anyone can recommend a padded bag to put a Maxi Cosi Cabriofix AND base inside to then check into a flight as luggage. For our older child we have the excellent JL Childress Ultimate Car Seat Travel Bag, but the Cabriofix will not fit in this bag with the base. On Amazon there are plenty of non-padded bags that do up with a drawstring, but they are pretty low quality and provide no padding or protection at all. Does anyone have any other suggestions? Thanks in advance.