Since AP already gets free parking (except for special ticketed events) the parking perk that I have used is free valet at the resorts with valet parking. When I went to PR yesterday to see the holiday displays and wander around, the guard originally game me a 3hr parking pass. When I asked about valet, she said - oh you don't need that then. I dropped my car off, and DD and I explored PR, GF, and WL all from the PR using the monorail and boats and did not have to worry about a time limit.
I have now used it at four resorts parking for the purpose of "seeing the holiday display". It kind of makes you feel "special" to have someone park and retrieve your car for you.... all for the cost of the tip!
I have not used it soley for dining at the parks, so I had not thought about seeing if they had special parking areas like the OP mentioned at EPCOT.