We did the ME from the airport to our Disney hotel and then a private car (limo) to the cruise terminal the morning of (10 am pickup) for an 11:15 PAT. Our departing flight left in the evening so the limo company picked us up from the terminal (8:30 am) and dropped us off at Downtown Disney. They kept our luggage in the trunk and picked us up later that day (2:30 pm) to go to the airport. This made traveling to/from stress free. We only had two large pieces of luggage and two small carry on pieces.
This company was recommended by our
travel agent and used personally by them. My travel agent vouched for them and I have known my agent for a long time. I wasn't concerned with leaving our luggage with them.
The driver did ask if we needed to make a stop or have him purchase beverages before our departure.