On the contrary, the airline has no problem with us checking it.
Since posting this thread, I have contacted
DCL by phone, and they are requiring us to carry it on. This truly stinks, since we will have the baby, the stroller, and only 4 hands. The food will take up more than half of the 1 carry on bag we planned to take. We will now have to have another carry on, which will prevent us from being able to bring on beer and pop, as we had planned, because we simply can't carry it all. Oh well.
We will further try to limit what we are carrying now by not packing dinner clothes in our carryons. In the event our luggage is not delivered in time for us to dress for dinner (which has happened before), we will just skip it.
According to Disney, the food needs to be x-rayed, which is why it has to be in the carryon. I don't understand why x-raying the food would be more important than anything else that is being brought on board in checked luggage.