Hi Lenny
We haven't done it yet, but will be staying in 3 different hotels in Dec/Jan.
I don't think there will be any problem leaving your luggage with the next hotel if it is too early to check in. Your room may be ready early, with a bit of luck.
We won't have a car either and are going to use taxis to change hotels.
We are planning to move onto the 2nd hotel early evening (having left our luggage at the 1st hotel and spent the day in the parks) and then moving onto the third hotel early morning, leaving our luggage there, going to the parks, then coming back to check in.
How many of you are there? If you have children it will take a bit more time to pack and pack again, but if you are only a couple it should be quite easy.
One tip I read on the DIS was to put all your dirty laundry and gifts bought in one bag so you know you don't have to unpack that bag again which is what i'm going to do.
If you have a week for each hotel that is great, we are doing three within 15 nights, so we'll see how we get on!
We are also finishing our trip on a high at the Polynesian, and think it will be worth the move from the Courtyard!
HTH