I don't mean to correct you, and I don't want to take the time to study it perfectly, but I think that Levi was set apart - He didn't get an inheritance, except a portion of the inheritance of each of the tribes... So Levi was scattered throughout Judah and Israel... I don't think Levi is counted with the House of Israel, even though a portion went into the diaspora with them (as can be noted by the identifiable Cohenim genes in far-flung places).
That doesn't go against your main point btw, as many were found to be righteous by YHWH prior to the crucifixion. I don't think that means they kept the law perfectly, mind you... but rather by faith (as is always the case)... Along with trying their best to keep the law, and repentance where needed...
Thank you for your response and I was thinking that Levi held no property and was not considered as part of the ten Northern tribes. had a senior moment...thanx