I believe you're reading the situation completely wrong here. In the scene, Jiraiya is explaining to Hazou why Hazou's conviction is not strong and pure enough to form or withstand aura. It doesn't matter who's aura Hazou is matched up against, Hazou will still fail due to his own weakness. Even though the Hagoromo are against everything that Hazou stands for, it won't strengthen Hazou's resolve any. Logically, he has more reason to fight oppose them, but logic isn't what forms a Jonin aura -- as Jiraiya explains himself.
An aura requires fanaticism, single-minded devotion, unshakeable confidence. Hazou believes in and is passionate about Uplift, but not to the point where it could be the only thought in his mind at a moment. Uplift is also an abstract concept, and harder to apply to a direct confrontation. Hazou would need to see the opponent as nothing more than an obstacle to Uplift that must be removed, and he can't compartmentalize and dehumanize an opponent to that extent yet.
Furthermore, Hazou doesn't actually have much killing intent. He gets angry and can want revenge on people, sure. But Hazou's focus doesn't compare to Keiko's, who has her own fledgling aura despite being a chuunin. To me, it seems that Hazou is willing to kill someone, but doesn't focus on the kill itself, since it's usually a means to an end. Iirc, Hazou experienced Orochimaru's Jounin aura/killing intent felt like all the different ways Hazou would be torn apart and ruthlessly dissected.
In order to acquire an aura, I think we'd need to change the way Hazou thinks and feels, especially with regards to his core resolve. Hazou strives for Uplift, but can we/he say he has unshakable confidence in it? I don't think so. I don't see a great way to change Hazou's resolve either. As players, we can make plans and take actions, but it's much harder to dictate what and and how Hazou thinks and feels. (If that were easy to do, we could turn Hazou into a hyper-efficient sociopath that could voluntarily choose to be freed from the restrictions of empathy at will.)
We've seen plenty of times that a Jounin aura has lingering after effects. Hazou/his clone would still be reeling and incapacitated after the aura passes. And then we'd get punched in the face.