I did read in one trip report that during the mid summer, the RPH was full on 2 days. They, the valet employees, did take the cars to another area and the owner was not charged for that valet parking.
The parking lot at RPH is large.
If you have the HP card or plates, use them.
Always talk to the front end manager at the hotel if you have issues over parking. Such as, no HC places available, would need free valet as someone in your group has mobility issues, etc.
I found that when I did use a rental car, the only times I left the resort parking was maybe one time during the trip.
Did a run to a local store and had a dinner out that evening.
The park is small and the hotels are on the edge of the parks.
You can walk or take the water taxi to get to the parks. You don't have to drive to the parks.