We went the first week of March 2003 (and always have, since I was a child) and plan another trip for March 1-9 2004. We stayed at AKL and had no problems there with crowds, although on the Sat. and Sun. the hotel became noticeably (but not badly) more crowded -- the effect of local tourists we were told. As for the parks, we followed the advice of folks on this board and the touring plans in the UG and had no problems at all. Could we do anything we wanted at any time of day with no lines? Unfortunately, no. But I can't recall even one moment of thinking "This is insane." And people had told us to be worried because it was spring break for U. of Florida!
Weather was PERFECT as usual for us in March.
Good luck!