On move day:
Call Bell Services and have them come pick-up your luggage and refrigerated items. Be sure to inform them that you have items to keep cold, if you do.
Tell them where you are transferring too.
Check-in to your new resort.
Go do whatever you want that day.
After getting your room text and you are back in it (items are not at your new resort until 2 - 4 PM), call Bell Services to have the items delivered to your room.
NOTE: You must be in the room for the pick-up and delivery. Tips expected.
If you want to go straight to the parks and not go to the resort first to check-in and not get the text, yes you can do that.