I'm a little frustrated that we have to talk to Zuko this loop, even if it's important, because the person who can make the most impact on Azula' situation is Sokka. This takes a bit of explaining, so please bear with me.
First of all, our understanding of what to do is based entirely on Meta-Knowledge. We are familiar with Groundhog Day, therefore we know the way to escape a time loop is to become a better person. However, Azula has no reason to think this, because time loops aren't a thing in Avatar. In addition, not every loop works like this, and I can name at least one case off the top of my head where the loop had nothing to do with the person looping.
In 'The Suite Life of Zack and Cody; On Deck,' the cruise ship gets stuck in a time loop when it is struck by lightning while crossing the International Date Line. Cody is the only person who remembers, but the loop was entirely unrelated. He escapes by studying it and altering the course of the ship, not becoming a better person. Therefore, assuming Azula needs to become a better person to escape isn't logically sound. It's a guess, and not necessarily a good one.
Aluza's first real step should be to study the loop. Poke it, determine its exact effects and see if she can find any limits. It seems to be inescapable, but she hasn't, say, tried boarding an airship and spending all 9 days running as far to the West as possible to see if it has an edge. It probably doesn't, but you can't make assumptions here.
Not to mention the list of entities who could make a loop like this happen in universe is pretty short. A spirit of time could do it, and that's about it. If Azula learns who created the loop she could just ask them point blank what she's supposed to do to get out of it, cut out all the guessing.
However, Azula has close to the worst possible mindset to do this kind of analysis. She's a Firebender, Strategist, and Politician, all of which are focused on making the world bend to your will. Being able to ask the world a question and listen well enough to understand the answer is an antiethical skillset to that, as the latest chapters prove. Therefore, she needs to talk to someone who does have said skill.
Someone who is good with outside the box thinking. Someone who has a knack for unconventional solutions and asking the right question. Someone who would find the concept far too enticing to refuse to think about it. And most importantly of all, someone Azula is willing to respect enough to talk to.
Out of the entire cast Sokka is the only person who stands a chance of not just escaping a time loop, but understanding one. He may have no bearing on why Azula is stuck like this, but he is the person who can figure out how she got stuck, and give Azula a path to follow.
TL;DR, Azula has an unconventional problem and needs an unconventional solution. Sokka is good with both.
As for the vote, I don't have an opinion here. The past is likely the best starting point, but the past includes their mother, who Zuko can't think ill of even if deserved. And the other options are a bunch of guesswork about what they'd turn into. I'll save my vote for when I think I can make a difference.