Epcot preferred parking in the afternoon?

[GlowingEye]

This is kinda last minute and maybe a dumb question, but what's the preferred parking situation at Epcot like in the early-mid afternoon? I've seen some reports that people have been able to park there without the up-charge later in the day. We're heading there tomorrow, and if we were going in the morning, we'd likely just gamble with regular parking, but the farther lots are a bit much for me (I rent an ECV inside).