You could easily come up with a story that resembles the one we got, but stitches it together more soundly.
Here's my idea:
Kirk's cheat in the KM test is a lot less obvious: he sets it up so that one of the cloaked Klingon ships has a fault in its cloak, giving Kirk a heads up and letting him blow up the Klingons before saving the KM, earning him a commendation.
Spock figures something is up, takes a look at the coding, and takes his evidence to the head guy, who basically lectures him on how life/space combat isn't fair. Spock is pissed because Kirk cheated and got away with it, and is displeased by Kirk's assignment to the Enterprise.
After Vulcan turns into a black hole, Kirk and Spock argue, but it doesn't get to point where Spock nerve pinches Kirk and dumps him on Delta Vega (it needs another name). Instead, Uhura picks up a distress call on the surface, which Kirk checks out in a shuttle because Spock pisses him off. The shuttle crashes because the pilot sucks at flying in arctic conditions and Kirk finds Spock Prime.
It turns out Spock Prime turned a holoprojector Nero left into a comm. device and gives Kirk the story of how he ended up in the past. Spock adds that the Romulans probably did something to that star going nova, because it started putting out pulses of energy at FTL speeds, which is what fried Romulus before Spock dropped the red matter into it.
So instead of going to the outpost, giving Scotty a formula he hasn't made yet, and beaming onto an Enterprise travelling at warp, Kirk asks to get beamed up with Scotty and takes things from there.
The only other thing I would add is Nero's idea that the Federation was behind Romulus getting fried, which explains why he didn't go blow up that star as soon as he got the Jellyfish. If the Federation can turn stars into FTL energy pulse generators of doom, then the particular star doesn't matter; so to Nero, blowing up the planets of the Federation makes sense because he doesn't know which one developed that tech.