March 11-18 will likely have the highest crowds of the month, in large part because it's spring break for most Texas public schools (in addition to other US districts and parts of Canada). The rest of the month is predicted to be slightly less crowded -- crowd level 8 instead of 9 like the 11-18th.
However, the weather is usually nice that time of year, which can make the crowds more bearable. With a good touring plan, it's manageable.