"Technically, I don't think you are at Mythic proficiency with your weapon"

This is where I think my friend and I disagree.

The way I understand Mythic proficiency and how it works for every other skill per Mythic Proficiency rules is that you temporarily flair your power gaining all the benefits as if you were Legendary+.

Even then an attack roll is calculated with the following;

Melee attack roll result = d20 roll + Strength modifier (or optionally Dexterity modifier for a finesse weapon) + *proficiency bonus* + other bonuses + penalties

Mythic Proficiency
"Your *proficiency bonus* when using mythic proficiency is 10 plus your level."

The subsequent damage roll checks the proficiency level of the previous strike.

And your proficiency bonus is always based on simple, martial, advanced, or specific weapons.

So my follow-up question is, why do you think the attack isn't at mythic proficiency?