Eeyore1954 makes a good point. Although they let people in through the World Showcase and direct them to Future World before 11:00, and I not 100% sure that you can do the reverse. I find it hard to believe, however, that if someone wants to go to BC/YC or BW from Epcot before 11:00 that they would be prevented from walking through WS on the same path that people are walking in the opposite direction. I agree that you should call to doublecheck, but I can think of no good reason why they would not allow it.
If you can do it, you should leave yourself at least 15-20 minutes to walk from FW to BC (add another 5 to go from the parking lot to FW, plus time to go through the entry gates and have any bags searched), assuming you don't want to have to hurry. When you leave Epcot, make sure you get your hand stamped. I hope it works out for you.