Here is a breakdown of some of the WDW car services and their costs for your trip. You would need to use a luxury van or a limo (more $$) to transport everyone safely. Most car services offer a complimentary 30 minute grocery stop as long as you tell them this in advance.
FL Tours (DIS Sponser) Round trip $109 + tip w/coupon
www.fltour.com
Yourride Round trip $ 90 + tip (it says it offers the same price for town cars & luxury vans on their site?
www.yourride.net
Tiffany Town Car Round Trip $90 + tip w/coupon
www.tiffanytowncar.com
There are others available too, you just have to pick whichever you feel most comforable with based on what you read, etc... At one time or another someone has posted good and bad reviews of them all, you just need to be prepared to deal with the company (take the phone number, comfirmation #, etc.. with you) and always confirm the car service before you leave for your destination.
I would recommend a car service over Mears any day. We have noticed in the past when arriving in Orlando that we can stop and get our bags, use the car service, stop at the grocery store and still arrive at our hotel much faster than those on Mears ( we have seen people arrive much later than us and we always stop for groceries!). So the overall cost is just something we
budget for when planning.
With the amount of people you need to move it seems that the car services would be the least expensive option.
HTH!
ALSO-
Welcome to the DIS!