Well, the only time your bags will be in your room, before you are there, is when you use DME. Resort to resort isn't going to get bags put into the room without you being there to hand over a gratuity....sad but true.
I have never, ever had my bags by 4pm. Usually after 5, and that's even with handing them off to Bell Services prior to 8am!!! If you are going to need anything in those bags, I would really recommend taking a cab or uber to the Polynesian first thing in the morning and then taking the monorail back to Epcot. Or, just leave your bags with Bell Services at BC, and when you're done at Epcot, uber over to the Polynesian with your bags from BC. That way you'll have access to your bags when you need them.