It would probably be best to find a way to go back to iOS 8.1.3. The Appradio 2 hasn't been supported for two generations now (the worst part about Pioneer). I don't think there's much chance to get it compatible with iOS 8.2.
I had an AppRadio 2 that I recently replaced with an AppRadio 4. When new iOS updates were released I waited until somebody could confirm that it worked with the same setup as me. I was using an iPhone 4S since it was released! It was tough to wait it out, but then I had to step into 2015 with an iPhone 6 and AppRadio 4. Technology just moves very fast these days. Luckily CarPlay should be a little more future-proof. And if the phone integration stops working with the AppRadio 4, you've still got a fully functional NEX-style interface to use (Bluetooth audio, USB x2, AV inputs, HDMI, AUX jack, etc.). I know with the AppRadio 2, once the phone doesn't integrate, all you're left with is a pretty bad AM/FM tuner (and a clock).
I hope you find a fix but it doesn't look too promising.