Honestly, going off of something I heard Fr. Stephen De Young mention in one of his podcasts. If I remember right, he says when you see the 12 in certain icons, Paul is often present instead of Matthias.

He did not speak of casting lots as being something never endorsed in the Bible, more just for this particular passage, it might not be the takeaway Luke is aiming for. Agree with all your points on 'chance' often being used in scripture.