I didn’t have experience with this but you can always take the Skyliner to DHS early and walk to Epcot, it’s about 15 minutes between the DHS station and the Epcot station if you take the shortcut through Boardwalk
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Epcot is mobbed by 11:10 and MUCH less busy after 6 right now so I’m not sure Rope Dropping is a super efficient touring strategy but if that’s what you want to do you can give it a shot.
On May 4th we got to JIA at about 6:20 PM and did JIA, Soarin, Nemo, Nemo again, SSE, Mission Space Green, and Test Track before park close at 10 AND spent at least 30 minutes looking at fish in the seas pavilion. And we weren’t baking in the sun. YMMV.
(this advice will be worthless once fireworks are back and people start staying until close again)