If it were me, I'd do it on your Epcot day. Go to Epcot in the morning, and then sneak out for an early lunch or dinner by going through the International Gateway to the BC/YC resorts...then just walk back to Epcot to finish out your day.
It really is a very short walk...not too much different than walking from, say, Soarin' over to something over on the far end of World Showcase.