You saw the Illmatic influence immediately though. Mic Geronimo, Fat Joe, Raekwon, Prodigy, Big Pun, etc..have all directly said Illmatic influenced them heavily. Pun out his own mouth said the second verse of Memory Lane is what made him start rapping
Plus let's not forget the "super producer" album. Illmatic was really the first album to have all the big producers work on it. Back then it was usually one, maybe two producers handling the majority of the production on albums Illmatic was like the first one to have star-studded producers throughout.
I think you're talking impact more than Influence. Paid in Full and Criminal Minded are the only two off those list that I feel influenced the East Coast as much as Illmatic. The other three are legendary albums, but I don't think they influenced the sound or how people rapped like Illmatic did, at all. Run DMC, LL didn't even have their own styles really. Run DMC took their style from Cold Crush. LL got his style from Kool Moe Dee and Silver Fox and a little bit of Caz.