I would suggest you start looking for info at America's Great Loop Cruisers' Assn - America's Great Loop Cruisers' Association
I researched this once and came away with the impression that you drop the mast to the deck in Chicago and turn back into a sailboat once you hit the Gulf. I have also read where some people drop the mast, ship it to the Gulf and step the mast when they get there.
Along the, you have to time your trip so you don't arrive below a certain south latitude during hurricane season or you will have all kinds of insurance problems.
There are quite a few blogs out there that report on indiviual trips people have made doing the Great Loop and the Lake Michigan to the Gulf is just one portion of that adventure.