Are you staying onsite? If so, just get up early and make it in time for that EMH. You'll be way ahead of the game and ready to hit World Showcase at 11:00. WS will stay relatively uncrowded for a couple hours too. Then I might be tempted to take a resort break, a ride the loop monorail break, hop on the boats to HS and just stay on to come back break, or a mid-afternoon TS break. There are also all the inside movies around WS which can give you a bit of a break from the crowds. You'll be fine.
If you're not onsite, make your FP+ for the morning and do the same thing. Enjoy!