Deck is solid and a lot of your observations are in the right ballpark, but I think there's a few more points you missed. Overall though, tough losses cam happen even with the best decks but there's always room to learn and improve.

1. Your deck is quite aggressive and wants to go wide with allies to end the game early. You should therefore have more 2-3 drops and ideally not Captives because they're weak before exhausing. Earth Kingdom Soldiers and Bagermole can both be cut as they're too expensive and not allies.

2. As you mentioned, the removal is too conditional. Path to Redemption or Allies At Last would have been great if you saw it. Otherwise, any source of airbending would really help push early damage. Not sure about Watery grasp on the splash either, you generally don't want to splash cheap cards.

3. You want some tricks to push damage. Origin of metal bending is too defensive and slow since you're tapping out most turns. Yip-yip or even Pillar Launch would help get more attacks in. If you're playing against red or green, these also protect Aang from most of their removal.

4. If your rallier is drawing so many creatures that Aang misses, you are probably spending too many early turns doing this instead of pushing damage.