Mears (who runs DME) used to and still does provide a separate shuttle service. I used them when arriving via Amtrak in 2011, and before DME used them constantly.
A limo/van is going to be your best bet. Not sure why you don't want to use DME but that's your choice. Because you have a larger group, a larger vehicle has to be brought in. You 'might' be able to get a Mears cab/Yellow cab that's a van that might fit your group. But, it's not going to be particularly inexpensive.