Glad you had a great experience. This is sort of piling on other posters' skepticism and I apologize in advance. This school may ultimately turn out to be a fantastic fit for your son. But please continue to take heed with the interpretation of "coach speak" from others who have long since been down that road.
Love your enthusiasm and excitement and it does sound like there are many positives. But, while the coaches spun it well, there ARE two teams and a huge roster. That's already been well covered. A few other things to note...
Two brand new coaches might just nail it and be great. But odds are, once the honeymoon is over, this is likely to be short lived and there WILL be learning/growing pains for them the first few years. It typically takes a few cylces for new coaches to figure out what they can and cannot do (administration/school/department hurdles). It can be even more difficult if both primary coaches are new, let alone very young.
"One team ... same coaching staff." 60 guys coached by 3-4 coaches makes it very difficult to drill down to personal instruction/development.
"not going to cut anyone that is putting in the work"... most likely means that roster size will not shrink as much as stated.
"... just don't expect a reply any time soon." is not something a coach would say to any player at any level if he is particularly high on the player.
Lastly, be aware that while there may not be a quota at this school, D3's/private schools greatly benefit financially from having large rosters of student athletes who are paying some or all of tuition fares.
Again, I could easily list more positives than red flags... just trying to advance your awareness and knowledge as you go through these visits.
Best to the two of you as you navigate the path!