What hotel and more specifically what part of the hotel is closest to Epcot?

Yeah, I've stayed at all 3 in the past. If staying multiple nights, the Dolphin/Swan is not a bad option either as it's right in the middle of Hollywood Studios and Epcot. It's technically off-property so you don't get the magic hours but you do get Marriot points for it. I got it last year for 330 a night.

Beach Club is closer, room 1501 is the closest room on property to Epcot but you arent adding 10 minutes by staying at either room at either resort.

Room 1501 at Beach Club is .15 away from the security check at the International Gateway

Let's say you're staying at the beach club villas on DVC points, the walk is still less than 1/2 mile

The walk from the furthest room at Boardwalk near the tennis courts is .57 miles BUT you're closer to walking to Hollywood Studios (which makes Boardwalk our favorite)

That being said, they do not guarantee requests specific rooms, floors or even buildings. Touring Plans has a feature that will let you scroll through and fin specific rooms and enter your requests there and they will make your request and I have had pretty god success either getting the exact room I want or something very very close but it's still not a guarantee.

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Dolphin and Swan and the other one is pretty close to the back side of Epcot by the French area. East to see the fireworks at close and bail out the back by boat or walking back to the hotel.

If you choose Boardwalk, the DVC section is a bit closer to EPCOT than the hotel section.

You’re right. I was thinking of it from the perspective of the front entrance vs the Boardwalk side. Good catch.