You don't have many options, but what if one of the adults in your party books a new ticket on a different airline for departure one day before, and re-book your Disney package to arrive one day before, then have that adult check-in on the 27th. Everyone would get the
free dining as long as at least one person is there to check-in on the 27th. This may not be possible for you and you would have to do the math to make sure the food savings on free dining would be in excess of the cost of the new plane ticket for the adult arriving one day early, and of course the cost of one extra night at the hotel.