I would also recommend diving into other Greek works. A couple graded readers that you may find helpful are:

Hellenistic and Biblical Greek: A Graduated Reader

https://www.amazon.com/dp/B00JXIIBDI/

A Greek Reader’s Apostolic Fathers:

https://www.amazon.com/dp/B07JN8TQ4P/

The first of these two even mentions the familiarity with the Biblical texts issue in the Preface.

Books by Geoffrey Steadman also look interesting:

https://www.amazon.com/stores/Geoffrey-Steadman/author/B00BXINVYU

While I have not read any of the above books yet (other than parts of previews), they appear interesting and I plan to get into them bit by bit once I finish Athenaze.