I'm the owner of an AppRadio 2 (two in fact!) and also a 64gb third gen iPod touch.  I'm aware they don't work in app mode but I don't know why (other than arbitrary reasons on Pioneer's part).

I wonder if anyone has looked into what is the problem, and is any workaround possible e.g. similar to AppRadio extensions on Cydia?  Or is there any information on the protocols available online to get me started at hacking together a solution?

Support for the video mirroring that the AppRadio needs for its functions was not possible till the 4th generagion devices (iPhone 4/iPod touch forth gen). You should still be able to use the iPod application, which the AppRadio 2 supports any 30 pin iPod for, but other functions are simply not possible.