Paul, the unstepping will be required to get you from the lake into the Hudson. Once you are in the Hudson, you can get all the way to Florida without worrying about height or depth. (Although, there are always ways to run out of water in the intracoastal if you try.)
Watch out for barges and tows, stay clear of the commercial traffic, and make sure you are lit up when you anchor. And of course, don't anchor in the spots marked "HERE BE DRAGONS" they tend to get cranky when hit by anchors.