Is there not a rental car agency at the Swan/Dolphin? National? Been a while for me.
Follow your plan, then drop off there at 7:45 or so and walk to back entrance of EPCOT.
It's possible you can get Disney to pick you up at the airport with Magical Express for free very early Saturday. So you wouldn't have to rent a car at all; just stay at an airport-area hotel with shuttle Friday night. Might have to get up pretty early, though.
Or stay Fri. night at a Disney hotel (cheap one, probably) and have Disney transfer your luggage to WL for free on Sat.