My Maryville team currently has a 4-4-2-2 structure (although that is prone to change, because I redshirt a guy most years but not every year) and is definitely on a pretty good run right now. We have won titles with only four upperclassmen.
That said, it's hard for me to really tell you the secret, because I don't know it. I've definitely taken my fair share of low WE guys, so it's not just like my guys develop super quickly. And it's not just clever coaching, because I haven't been able to duplicate it with any other team. I think it's just a combination of numerous factors including both skill and luck--what recruits you're able to get, what teams you end up facing in the NT, etc.
With a 4-4-2-2, I definitely think that you should be able to make the NT every season and possibly make the 2nd round every season if you're really good. As for streaks of Sweet Sixteens or Elite Eights, I know coaches who have them, and I have had them myself (in addition to Maryville, I had five straight Sweet Sixteens with Greensboro, but that's over--my Greensboro team isn't even PIT-worthy this season), but I think they depend in large part on just having players who can contribute unusually well as freshmen and sophomores. I have not been able to make those runs consistently in different worlds. There are definitely coaches better than me, and maybe some who can do this consistently in multiple worlds (jsajsa and tianyi come to mind), but I honestly don't know how it's done.