I think this deck has few big problems beyond needing a win condition.

First, your deck has 18 creatures + your commander. This might work in a control deck, you seem to want to play angel tribal, so this is a really low creature count.

Second, your land count is a little low. In the playtester it seemed to work out ok a decent amount of the time, but only with the red loot spells. Some are even cycling lands, which kind of makes things worse. Personally, I like 34-37 depending on various factors.

Third, Panharmonicon has almost no interactions in the deck. The only one that has much of any payoff is Thalia's Lancers. It is a dead card otherwise.

Your gameplan leans heavily towards having creatures to protect, but a majority of them cost 5 or more, so you lack early game presence. You also can't really rely on you commander flashing in if you need to play to have any blockers...

Anyways, I'm coming up blank on a good wincon. Maybe Warstorm Surge and similar effects?

1empyrean, thanks for the advice! Unfortunately, Angels are not aggressively costed, so early game is mainly going to focus on setting up mana. I will try adding in more lands and ways to ramp mana (despite the lack of options) to compensate the early game better. Most likely gonna combo Warstorm Surge with Fiery Emancipation.

Well, the angels theme is never going to be the fastest, though Kaalia of the Vast would be a better, if expensive, commander for the theme. If you really want to embrace the theme, that's who I recommend using, but Its understandable if you don't want to switch.

I like Archangel Avacyn  ^Flip, but she isn't really an angel tribal commander, given how her flip ability triggers. Maybe try building around the ability as opposed to a theme if you want to keep her as commander.