I have used Magical Express 4 times now(yeah I'm on the frequent flyer plan)...I have always had great experiences with it. From the point we arrive at MCO, go down stairs, check in, get on my bus line then boarding the bus has been 1/2 hour max. Perhaps we sit another 10 minutes waiting for a few more passangers...but we are relaxed. Then it is off to the hotel(3 stops max...and really it is not that bad). I always pack what I need for the first 6 hours+medications+toothbrushes/toothpaste. In your case I would pack pajamas and toiltries(and poss. a change of clothes for the morning-so you don't have to wait on the bags to get out), and ask for the luggage to be delivered later or the next morning(tell them when at check in).
Prior to ME I always used a town car...but you have to wait for your luggage to come down the belt, your driver is usually there, and then it is straight off to your hotel
Comparing the 2 a town car is quicker, by about 30 minutes-due to the extra hotel stops-YMMV(depending on how quick the luggage is and what hotel stop you are-once I have had the luggage take an hour to get off the belt), but ME is very easy to use-plus you don't have to transport the bags...and besides saving the bellservices tip, you also save the car service tip(and expense)-so for me the ME wins out!!!
If you are truly worried about this I would consider renting a car for 2 days(day of arrival and day before departure)...you could leave your bags in the car if you had to -exhausted-and poss. go to a market the next day)
Good Luck what ever you decide.