Well fiddle sticks. We'll be there 04/06 for dinner (clam bake) and Illuminations Cruise so valet parking then won't be a problem. But 04/07 will be a late day for us ... don't plan on hitting Epcot until the WS opens at Noon. So I assume parking at Epcot lot will be atrocious by then, and my knee will be having fits about walking around the park let alone the parking lot.
My DH has an AP so Epcot parking is actually free, but we were thinking it might be worth spending the $$ to valet park this one day that we know we'll be late (all other days we plan on hitting the parks before they open, so parking won't be as big an issue).