AAX DSP code is in fact written in plain c, with the exact same processing source code used for native (compiled using XCode/VS) and DSP (compiled with the TI compiler). It is actually more cross-platform, not less, because it is a very tightly constrained subset of what you can get away with on the native side.
But the existing JUCE AAX wrapper does not adhere to every aspect of Avid's AAX architecture. Loosening those constraints works fine for AAX Native and makes it much more similar to other formats (AU/VST) but alas means the wrapper doesn't support AAX DSP, and would require considerable changes in order to do so.
You'll also find that the Avid SDK examples which use JUCE (for GUI only, not the wrappers) use version 1.53 -- woefully out of date. And given the JUCEquake and major restructuring of JUCE that has occurred since, getting them to work with the current tip is non-trivial.
It's unfortunate that there appears to be little to no direct cooperation/collaboration between JUCE and Avid - this seems like it would be a win-win for both.
Alas, for now you're left to find your own solution. And maybe poke Avid to update their examples to a modern version of JUCE.