Lots of ideas for initiative bonuses here. You could consider, "When you can see your opponent at the start of combat, add Wisdom to your initiative rolls," but it might need something more. Maybe that'd be part of a level 3 feature that could be built upon? (This does raise the question of fights where you can see some opponents but not others, but I just wouldn't worry about that.)

As for the Iajutsu strike, it seems most natural to me to just give a huge bonus if you're hitting someone before their first turn in combat. And maybe a chance to parry if they're hitting you before your first turn? That way, you'd benefit from your quickdraw even if you lost initiative.

In the past, I've thought about doing Iado as a feat, fighting style, or Battlemaster maneuver. When it was a maneuver, I said, "If you hit a foe with a melee weapon attack before their first turn, roll (but don't expend) all of your remaining superiority dice and add that much damage." Honestly, that kind of undercuts the I-can-go-all-day aspect of the fighter, though.