I took my time getting off the ship. I walked off around 9am, but could have stayed on longer had I wanted to. I could have probably stayed on until 9:30am. People were still in Cabanas when I left the restaurant around 8:45.
I actually sat outside the
Disney Cruise Line terminal on a bench with my 2 boys waiting for my DH who arrived around 10am.
Had I only been getting off and heading over to the terminal for my Royal cruise, I probably would have made my way over by cab around 10am. If you couldn't get in at that time, I would have sat outside for a bit. Their are many shaded areas to sit and relax.
I personally don't think it's worth it to rent a car or go anywhere for a few hours.
I was sitting in the waiting area, already checked in by 10:45am, so even if you had to sit outside for say an hour or so, it's worth it in my opinion.
Just take your time and slowly make your way over from Disney to Royal.