Paul and Ignatius/Polycarp or references to Pauline controversy in general.

EDIT: Maybe Polycarp isn't really a contemporary to Paul, but Ignatius should have been aware of Paul during his ministry and the controversy surrounding his apostleship.

Recently I've been doing a lot of research on Paul for a historical fiction comedy book (inspired by the idea that Simon Magus is intended as a parody of Paul), and have been asking the question of why there aren't many references to Paul among his contemporaries like Ignatius and Polycarp.

I know that it's believed that the majority of Ignatius's letters are pseudonymous (I don't know nearly enough about Polycarp yet). However even in the genuine ones I find it odd that neither appear to have talked much about Paul or gave any kind of critique or defense of him. Especially if there was a supposed rivalry against Paul and the likes of Peter and James.

It's obvious that Ignatius was at the very least aware of Paul by his quoting of 1st Corinthians, but you would expect him to address Paul with how infamous he should have been, by pretty much taking the church from under Peter and James's feet and turning it into pretty much his own thing (my interpretation based from the genuine Pauline epistles and the stories of Simon Magus).

Am I looking at this the wrong way? Or is it possible that there was a lot more critique/debate surrounding Paul by early church leaders that we just don't know about because Paul's theology ended up winning out in orthodoxy.