We own and Expedition and a Dodge minivan. The seating configuration is the same. (2+2+3) The Expedition has less room for luggage than the minivan. Behind the third seat there is a about an 18 inch space between the seat and the rear gate. You can line up three normal (carryon) sized suitcases up side by side. Of course you can pile duffles on top of that. The Dodge Caravan has a much larger space. The only advantage to the Expedition is the luggage rack but you need to check the company policy on using it.
I feel your pain. We always end up having the same situation (more luggage than either can hold). Here's what we have done on occasion.
1. CRAM! JAM! Bags in laps; sit on bags; bags piled to the ceiling.
2. If van has luggage rack - I bring those ratcheting type straps with me. If the van has a luggage rack I strap as much as I can on top. Sadly, lots of time the vans do not have a rack.
3. Make 2 trips. 1/2 the family and their bags are dropped off then circle back for the second group.
4. Lastly, 2 rental vehicles. Normally we travel with my sister's family. They rent a vehicle as well. We fill one vehicle with luggage and the other with people.
Honestly, we choose the van when on vacation. Z Classes are normally considered a premium rental and cost more.