I'd suggest the economy lot. The buses have been revamped starting late 2018. They come very frequently, hold approx. 20 people, and would have space for your whole family. Under the new system, we rarely wait more than 5 minutes in either direction. You'll save money and I do honestly belive it would be less hassle than parking in E and moving over to B, or vice versa.
Otherwise, try Winner. They'll take you to the airport in your car and drop your car back off to you.