I do not understand where the idea that free archetype only gives six extra feats is. Maybe your group is using a variant of a variant. Standard free archetype, per the GMG:
"The only difference between a normal character and a free-archetype character is that the character receives an extra class feat at 2nd level and every even level thereafter that they can use only for archetype feats. Depending on the needs of the group and the theme of the game, you might restrict the free feats to those of a single archetype each character in the group has (for a shared backstory), those of archetypes fitting a certain theme (such as only ones from magical archetypes in a game set in a magic school), or entirely unrestricted if you just want a higher-powered game.
If the group all has the same archetype or draws from a limited list, you might want to ignore the free archetype’s normal restriction of selecting a certain number of feats before taking a new archetype. That way a character can still pursue another archetype that also fits their character."
And I think it was the confusion over "every level" was just a bit of unstated premise: that the "every level" in this case is "every level where you normally get new feats", so 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.