You'll have no trouble entering Epcot any time during the day. Obviously be prepared for insane crowds and high wait times. But this is where FP's and breaks come in handy.
MK is where you want to be there early because they start hitting phased closures on NYE pretty early.
I recommend heading to Epcot before 5 because they do some great fireworks at 6pm that you'll enjoy
"No trouble" entering. Getting to the entrance will take some time. In 2014, it took us about two and a half hours from Bay Lake Tower through the gates at Epcot around that time of day.
Unbelievably crowded doesn't even come close to describing it. We've been to all of the parks on one holiday or another and I have never seen a park so crowded in my life. Steer clear of WS, it was a madhouse.
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