Apple's own human interface design guidelines would forbid this. Your app can't encroach on the abilities of the OS that transcend your own application's responsibilities. The whole point is to have a consistent experience for the device and if you're modifying something as fundamental as switching apps, you're violating that principle.
If you can't exit the app, you're essentially turning your device into a single purpose unit. How do you expect to get back to the app list if you disable fast app switching and the home button?
Whatever solution you find would not be approved by the app store.
You should look at whether the current multitasking features can help chip away at your reasoning for needing the app to always run in the foreground.