How did Money rise to the top so quickly?

I don't think it's as quickly as you describe it. You have to remember that all the prison flashbacks happen basically over the course of 10 years. At the beginning he is only a small light in the gang, but he is earning himself into it for being able to do whatever it takes.

The turning point is the riot, though, where he attacks/kills an inmate and this way also saves the boss of the Latinos. But when this happens he was only there for about a year and he gets sentenced to 9 more years. Not only is this the point where he realizes that this isn't just a bad 16 months dream but ultimately the end of his life as he knew it (telling his wife "It's over. Forget I exist."), it is also the point where he gets in with "upper management".

We don't see much of these remaining 9 years (maybe not entirely 9 years, but at least 85% of that), but all of this time adds into him building hismelf a reputation. He's in with the big guys now and ends up working directly for the Beast after replacing Redwood as the guy "having the keys" to the place. He might not have done anything outside for the gang, but he's worked himself up for almost 10 years. Shotgun just didn't go a similar carreer promotion and simply didn't get in with the "right" kind of people. Afterall, as Jacob says at one point, they all started as some poor dude trying to survive, which is also a point about the US penal system the film is ultimately trying to make. So we don't really know how much of a big guy Shotgun really was beyond just having been in the gang already before Jacob.

And at the end of the day, Money was directly doing the deal for the Beast and when the Beast tells you Money is running the show, you don't question that order, nor do you question Money's.