IOS 4 Alarm Clock App with Multitasking Support?

I would say what you want to do is not possible with the current restrictions of iOS. That said you can probably fake a progressive alarm by doing what the developer of Progressive Alarm Clock do to play the progressive alarm. By scheduling many local notifications, one after each other.

He has divided the alarm sounds into chunks of say 10 s each with progressive volume levels. This is a very crude example to show how the progressive alarm can be faked.

Whatever the Progressive Alarm Clock developer is doing, it's not what Robert Höglund is describing, AFAIK, since the alarm will sound even if the phone is in silent, and UILocalNotification doesn't seem to have any way to allow for this. In addition, if you kill the app manually while an alarm is pending, the app will notify you that it needs to relaunch. This seems to suggest that it must be somehow running in the background.

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