I'd say the absolute worst thing they could do is move it off Memorial Weekend. Two huge things at play here, first is how many people would take a day off from work to be at the final four? I think that extra built in day off really helps a lot with attendance. I know dozens of people who probably wouldn't attend if they didn't have Monday off.
Second thing is youth leagues. If the tourney is say on the first weekend of June how many people have you eliminated because of youth lacrosse leagues on that same weekend? Personally speaking most of the Albany area youth leagues are off on Memorial weekend. Was there youth lax in Syracuse or Long Island this past weekend? Grades 3-8 ?
People may scoff at that like pop warner and soccer on a random fall saturday but it's a real issue. Myself as a coach and several others coaches and a bunch of kids can't exactly leave our teams on Saturday June 1 to go to the Final Four weekend.