I wouldn't count on Ubers. They are not nearly as prevalent in Edinburgh as apparently in other places. I wouldn't use anything other than a black cab if not using the bus.
There will be an absolute avalanche of people leaving the castle after the tattoo. Everyone will be looking for transport. If the ship offers a package including transport I'd snap it up.
PS as an Edinburgh resident I avoid the Royal Mile like the plague. It's jam packed with tourists. There are so many other, different, interesting places to go.
Good luck anyway.