Think I'll swap Larkus' desire to please people with Curff's intense curiosity.
So, starting with Curff, lacking that burning drive to understand things would change his history quite a bit. His need to understand his own powers became his obsession, and his failure to find an answer ground him down into the cynical, paranoid hermit he is today. Absent that quality, and with the added desire to please others, I could easily see him just staying with his tribe his whole life. That's kinda boring, though, so let's assume he still leaves. After all, he's still a sorcerer, he's still a bit dismissive of his people's traditions, and he probably still enjoys the intellectual challenge of magical academia.
So, off to the Ashen Hill. His added desire to please would mean he'd get along much better with the other students and teachers. With less focus on understanding his powers and a lot more on figuring out what he could do with them, maybe he'd become a teacher himself, even build a life for himself in the city near the school. After a time he might still become an adventurer, but this time he'd be in it for the stories and the teamwork. After retiring from adventuring he'd either return home to his tribe or stay in the city. Either way I have the adorable mental image of Curff making magical fireworks in the air to entertain small children stuck in my head and it's entirely your fault.
But yeah, if Curff even makes it to the PPC he'd be lacking much of the trauma of his life, and so a much kinder (if potentially less powerful) sorcerer more interested in experiencing the Multiverse than understanding it. Probably much less of a headache for his partner, too.
Now, over to Larkus. His desire to make people happy is a pretty integral part of his character, but I don't know if it changes his history as much as Curff. His added curiosity might bleed into some of his other passions like his love of the outdoors, but at the end of the day Larkus was born to be a cop. Fits his sense of duty, desire to protect people, and frankly, what other job might actually involve bar brawls outside of bouncer or bounty hunter?
So, off to the Academy it is. With a greater sense of curiosity and less focus on his social life he'd be a much more disciplined person, and a much better student, possibly earning a more prestigious posting out the gate. Things really start to change after that, though. Larkus is a smart fella, and more than dedicated enough to rise through the ranks, but his desire for a personal, on the ground connection to his community overrode his ambition, and his tendency to somewhat bend the rules did not endear him to the higher ups, so he never made it past Officer. With a more intellectual bent and less hijinks and community focus, he'd make detective for sure. Not entirely sure how that affects his service during the war, but he wouldn't be on the lower levels, which removes a pretty solid chunk of unresolved trauma. Of course that doesn't remove the even larger chunk of unresolved trauma that is Order 66, in fact it probably makes it worse since being a detective in the Temple District means he'd likely coordinate with Jedi on many more occasions.
So, assuming he again fell through a plothole instead of being shot as a traitor, he'd arrive a much less gregarious individual more focused on understanding the Multiverse and protecting the plot continuum, and quite possibly trying to lose himself in the work to avoid facing the realities of his entire life basically imploding. I mean he kinda does that anyway, just with more card games and alcohol, but in this version it's worse.
Huh. Just realized these two kinda flipped a little bit. Didn't see that one coming. This was a lot of fun, though. It was a fascinating character examination. Thanks muchly for posting it, Cal!
Also, please forgive any typos. Is very late at time of writing so at this point it's either post the darn thing or wait until tomorrow, which risks procrastination delaying it who knows how long.