You do not need park ticket to dine at the Contemporary. Since you have a car, I would drive and park at the Contemporary. They will give you a pass for parking. You could use Disney transportation. From your resort take bus to MK, (you will not go into the park) then get on the monorail to the Contemporary.
If your leaving from AK, you could take bus to the Contemporary, then after dinner monorail or walk to MK bus stop and get on bus to your resort. Unfortunately, there is not resort to resort transportation.