Since the OP is arriving close to the DME luggage delivery closing time, I would recommend getting the bags and bringing them to the bus with you. It will add about 15 mins to your overall time, but at least you will be sure you get your bags that night. Otherwise, you may miss the cutoff time and your bags won't be picked up until the next morning, and then they will be delivered to POR, not BLT!
The next morning, I would just hand my bags off to Luggage Assistence at POR. They will transfer the bags over to BLT. Or, you can take a cab, with your bags, directly to BLT. You may be able to get into your room earlier than the official checkin time, but I wouldn't count on it. Better to be pleasantly surprised if you do get in early.
You can get checked in, give them your cell phone number to call you when the room is ready, and then go off to a park. MK would make the most sense. The only issue I have with Disney moving the bags is that it more often than not, takes the entire day. I always hand off my bags by 7:30-8 and never get the bags in my next resort room until well past 5pm!!! Drives me nuts.
I am seriously considering just taking a cab, with my bags, the next time I switch resorts.