I don't mind using private API's or anything of the kind that Apple doesn't like, but would prefer a quick solution that doesn't stuff like playing silence in the background or swizzling.
Obviously this isn't for the app store so please no lecturing :)
So how do you run in the background without any restrictions like "backgrounder"? I didn't manage to find an answer besides some that point people to different directions, but maybe since then someone managed to dig it up already.
Depending on what your "app" is going to do, you can hook MobileSubstrate. This will load with SpringBoard and essentially run "in the background".
If you want to write an actual application, then you can also write a "Dynamic Library" which will be loaded with SpringBoard by MobileSUbstrate. You can talk back and forth between this dylib and your app by using NSNotificationCenter; creating and posting notifications.