The kids are 4 and under, so they can't really participate too much. So it's mostly adult games we're still looking at for when friends come over (or two player games).
You sound like my brother-in-law who owns over 300 games. But he's not a big BYU fan, so I'll rule that out. He has the One Night Ultimate Werewolf one that we've played and is fun (if I'm mistaken about your BYU fandom and this is you, then hey).
We do have Forbidden Island. I forgot about that one as I was just going off memory, but we do enjoy that one. The "work together" games can be hit or miss for me. I know a lot of people like Pandemic, but it's not my favorite. That might be because the two times we played it we did pretty bad. We also have Blokus, but I'm more into that than my wife.