you are absolutely correct, basketball is king but not for the reason at the aforementioned schools as you might suspect. The NE -10 or 16 was formed, was and is a scholarship basketball conference .It has morphed into a conference for all sports, including basketball but excluding hockey. It is a rogue conference, ie. there are no rules in the conference.Schools are free to give scholarships in any sport according to NCAA regulations that is why a school like LeMoyne college gives lacrosse scholarships and St.Mike's does not. The problem with reclassifying is that if you leave a league you must find another league(s) for all sports.
the schools are not going to reclassify for hockey in a league that is hockey specific, without having a viable option for joining a league for other sports.
From a financial standpoint right now DI is not an option.That may change but not in the next couple of years.