“I fear I told a little fib about my pony past
I hope that when you hear the truth, you will not be aghast”

Turns out that there might ave been other, more pressing reasons that Cheese left Manehattan; his sister.
In case you don’t know her (and most likely you don’t), this is Marine Sandwich. Well, Submarine Sandwich, but she changed her name because she refused to have anypony refer to her as sub anything. She’s featured in the official IDW comics, and is a… little crazy. She’s a ‘food performance artist’ who is so reclusive that the public has no means of recognizing her besides the red cloak she wore. That’s where Applejack comes in; mistaken for Marine Sandwich, she is thrown into the baking competition instead. Normally, hijinks would ensue, and they sort of do, but less hijinks, more psychotic rage. She declares that “And YOU who shamed me…. You will become my latest MASTERPIECE!”, referring to Applejack… and yeah, she does fully intend to do so. She has ego issues to boot; “I am the GREATEST GOURMET ARTIST Equestria has ever known!”. She also has a repertoire of absolutely batshit insane expressions. At the end of the competition, she ends up showing up with a massive frosting cannon that can freeze ponies in it, and starts spraying everypony in the audience, not just Applejack, declaring the newest dish to be ‘Fondant Fools’ as she tries to make iced statues out of hundreds of innocent ponies. Maybe psychotic revenge on Applejack would be less unreasonable, but taking revenge on… a lot of ponies. A lot of them, all innocent. Hell, AJ was innocent. But on to the actual point; I think she’s Cheese’s sister for several reasons. For one, they share a mane color, and, well, she’s a parallel to Pinkie just like he is; Pinkamena. She’s got a similar mane to Pinkamena, psychotic expressions, and an inexplicable high tech cannon. Now, where have we seen one of those before? Add in that she intends to serve up Applejack as a food dish, and you have parallels to Cupcakes!Pinkie. So…. yeah.
It also fills out something I’ve always found a bit suspicious about Cheese’s confession song. The massive gap in the story. Have you noticed it? Let me help:
“I fear I told a little fib about my pony past
I hope that when you hear the truth, you will not be aghast
I wasn’t quite the super party pony like I claim
The fact is that I was so shy, nopony knew my name”

“I stumbled into Ponyville one afternoon by chance
And found the biggest ever celebration party dance”

You see what I’m talking about? The big gap there? His reason for running away. He never mentions an actual reason for running away, nor even describing anything about his home. Sure, you could assume that being shy was the reason, but that’s not really a reason to run away. And generally, ponies who are so shy that they can’t work up the nerves to talk to other ponies don’t exactly have the confidence to run away in search of somewhere else. I don’t think he ran away for no reason beyond finding himself; ponies who run away at that young an age either end up coming home because they miss home, or have something worth running away from home to escape. And while many ponies are shy, not being able to speak to anypony out of fear is a red flag to me. So, he has an unexplained reason to run away.
And you know what’s a good reason to run away? Having a psychotic older sister who considers culinary arts a chance to freeze other ponies alive and serve them to others. I don’t exactly see her as… actively angry at him (more than she is at anypony else), unless he set her off, but just existing in such a hostile environment is good enough reason to go before she starts using her cannon because you didn’t like the dinner she made enough; “I MADE DINNER FOR YOU AND YOU’RE GOING TO EAT IT! You’re going to EAT IT and you’re going to LIKE IT!”… Yeah, that’s a reason to run away. Run before she makes you into an ice sculpture.